Erdogan's policies towards Turkish citizens are in general considered to be Authoritarian. This authoritarianism is generally attributed to Ergodan's hunger for power, and it is alleged that Turkey is sliding into dictatorship.
But, I am curious about an alternative narrative according to political science.
According to political science, Why can't Erdogan's dictatorship be defined as benevolent?
Of course Erdogan's dictatorship (although technically it is no dictatorship) can theoretically be defined as benevolent. It is solely a question of the definition of the "benefit of the population as a whole", to cite your wikipedia article. Depending on the viewpoint (or political agenda), some - especially Erdogan supporters - might say it is benevolent, others - say, Kurdish resistance groups - might say it is highly malevolent.
Typically, what is a benefit is defined by the political views of the observer. Calling a specific dictatorship benevolent or not reveals more about the caller than about the dictator.
Just to show some examples for things that people might see as measures for a benefit (although not every point will be a benefit for everyone and some even contradict each other):
The second problematic point is the question of who the "population as a whole" is. Are you including non-believers? Dissidents? Kurds? Kurdish resistance fighters? Syrian refugees? Should a benevolent dictator help the refugees, or should he try to expel as much of them as he can to protect his own citizens? Should he fight the terrorists of the PKK (or resistence fighters? Your mileage may vary...) as hard as possible to increase the safety of Turkish police officers or soldiers, or should he try to negotiate a deal with them? Are they part of the "population as a whole"?
As you can see, answering this questions is not easy, and it depends on the own personal values and political stance. You can clearly say that from the viewpoint of a typical Western mainstream liberal or conservative, Erdogan is not a benevolent dictator. But then, a (slight) majority of Turks loves him, as well as a majority of Russians love Putin (another non-benevolent dictator from a Western viewpoint). And those clearly think that he has done many things for the benefit of the Turkish population.
So my question would be: Who asks, and what are your values and personal beliefs?
"Benevolent dictatorship" is not very easy to assess (Wikipedia):
Many dictators' regimes portray themselves as benevolent, often tending to regard democratic regimes as messy, inefficient and corrupt.
Let's assume your propose narrative and compare it to a notorious Turkish leader that is considered a "benevolent dictator" - Mustafa Kemal Atatürk:
He presided over a series of reforms such as allowing women to vote, agrarian land reform, removal of Islam as the state religion and the establishment of secularism, and the adoption of a Western-based criminal code.
This BBC article catches a glimpse of some recent changes in Turkey:
Also, this article argues about Erdogan taking steps towards making Turkey an Islamic state:
Given Erdoğan’s record-setting jailing of reporters, his mass arrests after an aborted coup, and his frankly expressed ambitions to Islamize Turkey, these changes will result in a much more authoritarian and Islamic government incompatible with the West.
Clearly, there are some contradictions when trying to attach this label to Erdogan.
A "benevolent dictator" requires conditions that are difficult, if not impossible, to achieve in reality. Benevolence requires a dictator spending resources on promoting the public good. But as Bruce Bueno de Mesquita and Alastair Smith explain in "The Dictator's Handbook", a dictator must devote almost all of their resources to keeping power; if they do not, then they are at a disadvantage to a usurper who will. They must continually pay off their key supporters with enough money that the supporters aren't left wondering whether they could get a larger share by staging a coup and installing someone even more corrupt.
As an autocrat destroys democratic checks and balances, they their position becomes more powerful. While that may seem like a good thing (for the dictator, that is), it simply means that seizing power becomes more rewarding, and therefore more tempting, for their rivals and underlings. Adding more power to their position increases not only how much oppression they (can* do, but how much oppression they must do, because all of that power is then available to anyone who seizes power, and thus is available for a potential usurper to say to others "Look at all the things I can do to help you if you support my coup". Thus, if the position accrues more power that isn't spent keeping the position, that additional power actually makes the dictator less secure.
Spending resources on keeping power means not only distributing money to key supporters to keep their loyalty, but also optimizing for monetary extraction to get the most money in the first place. Thus, societal resources are not employed in whatever capacity generates the greatest output, but in whatever capacity generates the greatest amount of output that can be captured by the dictator and his key supporters. This decreases the general welfare so much that even if the dictator were to spend all of his spare resources after paying off his supporters (which leaves only a small percentage of the total amount extracted from the country) helping the people, it would not be enough to make up for the decrease in efficiency that is inherent in dictatorship. A dictator can be "benevolent" in the sense of being a tiny bit better than a purely selfish dictator. He can also be "benevolent" by being "merely" selfish, rather than sadistic or insane. But he can't be benevolent in the sense of being better than a liberal democracy.
The other answers put focus on the static picture (definition of the term "beneficial"; moral) and the dynamic/temporal picture (stability of dictatorship subject to socio-economic forces). I might also point out that there is a spatial picture.
Economists like to talk about opportunity cost/gain, meaning that it is not useful to assess an investment alternative as more or less absolutely good or bad. But rather it only makes sense to assess investments relative to each other or at least in comparison to an (almost) risk free investment. And these may be different across markets and may change over time. It just doesn't make any sense to compare today's rates of return on an investment with those that were possible in the 50's of the last century because the business opportunities that were common in the 50's simply don't exist anymore today. That's not a matter of theory but only good old reality.
In my opinion the same holds true with political systems. When arguing about Erdogan's regime it is pointless to compare it to any theoretical alternatives if it is simply infeasible to assume that there could be any other political system built around the same society of people with the same mindset. And so it is also pointless to compare Turkey with central Europe or the US because people from Turkey can't just go to CE or the US to make up some exile government business for Turkey. Likewise experience shows that it is highly unlikely that a dictatorship can simply be replaced by some sort of "peaceful revolution". Political overturn is pure violence, so the option is purely imaginary.
And finally one other thing that is highly underestimated is the cultural horizon. People living in Turkey might just don't know what they are deprived of under Erdogan. Equally well, we in central Europe or the US etc., might not know what we are missing about the advantages of Erdogan's regime. Freedom means responsibility, and many people are overwhelmed by the responsibilities that come with capitalism and political, economic and scientific progess. They are more than happy to bury their head in the sand. At which point we are, again, where there is no practical political investment opportunity to compare with.
For the records, I sincerely don't believe that I would be happy in Turkey or any other islamic country, but, as the saying goes, YMMV.
That being said, it is clear that people like Erdogan and Putin deliberately play their evil games with this ambivalence of political value and take it as the foundation of their disinformation. So as I see it, people in democratic countries have basically two disjoint belief alternatives:
1) succumb to the informational power of the dictators and think they could play the appeasement policy game
2) decide in favour of their own firm conviction in what they do is right and what the others do is wrong, and accept a certain probability that in fact they could themselves be wrong
I can hardly imagine how there could be anything inbetween. Since there is no complete information, it is a matter of who is more determined to win the battle for power over their own minds.
It is always a value judgement about whether a dictator is benevolent or even a dictator in some cases. Even Kim Jung Un has elections and claims to be working for the people's good.
But if you look at actions they have done. Edogan has imprisoned journalists for criticism (or stating factual observations). Unless you are willing to argue that the truth about Edogan cannot be known because that would destabilise the only man able to rule Turkey well, then the best you can say is that he is trying to spare his people the discomfort of knowing the truth.
That is at least one example of where he has leveraged his personal interests many times above that of his citizens.
Because if Turkish peoples try to call it that way, in Turkey, they end up in jail for saying that Erdogan is a dictator--- that is why the question asked according to political science, and not according to Turkish people.