First, the premise is not entirely true. To start with, it gives the example of Saudi Arabia, but Saudi Arabia only allows voting in municipal elections, while the national government is a hereditary absolute monarchy.
While "full" suffrage is ultimately more subjective and culture-bound than it might originally seem (Should children be able to vote? Prisoners? Chimpanzees and dolphins? Foreigners? Corporations? AIs? People with severe dementia or other major mental disabilities?), there are certainly countries that lack full suffrage by the standards of most other countries, even ignoring the hereditary absolute monarchies:
- Vatican City, a UN observer state, has a leader elected only by a special class of person that does not necessarily even reside in the nation, the cardinal. All the other priests and other people who live in Vatican City cannot vote in this election.
- Andorra, a UN member state, has two leaders, one elected by the French people—not Andorrans—and the other chosen by the Catholic Church.
- In many jurisdictions of the USA, a UN member state, people convicted of certain crimes cannot vote.
There is one country that has a maximum voting age, namely the aforementioned Vatican City, where the maximum voting age for the enfranchised population is 80.
Still, it is true that, by and large, most countries do have relatively similar voting criteria. In part, this is because of international law like Article 21 of the Universal Declaration of Human Rights:
The will of the people shall be the basis of the authority of
government; this will shall be expressed in periodic and genuine
elections which shall be by universal and equal suffrage and shall be
held by secret vote or by equivalent free voting procedures.
Overtly violating these rules could potentially lead to UN resolutions, sanctions, and so forth. Countries that that have never followed them, like the aforementioned monarchies, get away with it by tradition, but a country that tried to innovate such a system might face consequences.
In part, it is because of peer pressure and imitating the political systems of countries perceived as more "successful"; it may be particularly relevant here that the USA no longer has de jure poll taxes or literacy tests for voting.
In part, it may be because of domestic appeal. Maintaining the support of the general population is a good way to retain political power, and the general population likes to know that they will have a voice in government. Having fewer voting restrictions is a cheap and easy way to do this.
Less positively, it is because authoritarian governments have largely moved beyond crude disenfranchisement methods in favor of more subtle but equally effective techniques. A literacy test can be foiled by education; a poll tax can be foiled by charitable donation. Simply declaring a certain group should not be allowed to vote will attract international condemnation.
It's much easier, then, to leverage existing, relatively uncontroversial laws to try to disenfranchise people who vote the "wrong" way. For instance, perhaps the people who should not be voting are not really citizens, as with stateless people of Haitian descent in the Dominican Republic. Perhaps the election had voter fraud and was never legitimate to begin with—even better if your political allies are in charge of election authorities and can help prove it. Perhaps the candidate preferred by a group that you want to disenfranchise happens to be disqualified for whatever reason, as in Venezuela.