First of all what's the scale and scope of that question? The U.S.? All countries? All of history?
Also what counts as illegitimate? Officially overturned? Overturned afterwards? Annulled? Or just contested? Also in the case of 2016 there were many claims that the election was tainted, but the opposition conceded the election and didn't question it's legality. Which is much different from for example election fraud claims of the 2020 election where despite no significant facts hinting at violations of those 5 points, such claims were nonetheless made.
Like you seem to try to defend yourself against the obvious case of the Russian election where "reasonable exceptions" might have been stretched in order to keep the opposition off the voter roll. And where there might be some asterisks as to the "independence" of the invited observers. Nonetheless the points are still so broad that this might actually still be a valid example.
Also acknowledging the "legality" of a process might not mean as much as you think it does. This makes the underlying assumption that the process itself is legitimate.
For example while a victory via electoral college votes is not technically illegal in the U.S. it might nonetheless question the democratic mandate of such a president.
First of all the existence of faithless electors already casts some doubt as to what choice the people actually have in this election in the first place if they elect one person, who has one very easy job and blows it (to be fair some states have laws against that). Going to the fact that states have different voting power, so one vote is not equal to one vote. First-past-the-post-decisions where 50% of the votes can be ignored and can accumulate to an effective MAJORITY. Like do the math you can win 50+% of the states with 50+% of the votes each and thus end up with barely over 25+% of the votes, even less if you do it on the privileged states. And even less than that if you figure in techniques like Gerrymandering.
Now for the past century that hadn't been much of an issue, because the person winning the electoral college vote had also won the popular vote. That is until the very dubious 2000 election where the results were still very close but where point 5 was also very disputed.
And until 2016 when there was a clear electoral victory even excluding the unfaithful voters, but where the popular vote was significantly in favor of the other candidate. So a technical rather than a democratic victory, which for a self-proclaimed democracy could be a legitimization problem.
A similar legitimization problem could occur due to problems mentioned in origimbo's comment. Namely if the voter turnout is too low to represent the general public for example due to en.wikipedia.org/wiki/Election_boycott. In those cases the election might still be technically valid and is often treated as such by the government and their supporters, but draws significant doubt of legitimacy within the camps opposing them.
To that end voter suppression and voter indimidation could further complicate the matter. Now you explicitly rule out physical force, but there are other means to deter democratic participation. Requirement of documents that you know parts of the population eligible to vote doesn't have, making voting more cumbersome and expensive so that the poor can't afford it, etc.
And with regards to Russia interference, another point not covered in your initial 5 is disinformation which is also listed under election fraud. So idk casting doubt on absentee ballots during a pandemic making people chose between their democratic rights and their health. Or famously the claims of the Ukip Party during the Brexit referendum. While not technically violating your 5 points, changing what the vote means after it has been cast is a very good reason to question the legitimacy of an election.
Another example might be George Santos who apparently lied so much about his life that the House ethics committee expelled him. So does that count as an illegitimate election or is the election legitimate but the result rectified afterwards? And does that matter with respect to colloquial usage?
Either way in terms of disinformation campaigns that try to sway public opinion in one direction, an election could possibly be called illegitimate despite not violating your 5 points. Also worth mentioning, while a lot of these points aim at monkey business by one of the candidates (or their parties or government, etc), foreign intervention in an election is not necessarily an accusation of one of the candidates but a general problem for the integrity of the elections within a country.
So if Russia intervened and Donald Trump would have nothing to do with that, would not have known about it and just passively profited from it, he would not be the culprit and wouldn't have done anything wrong. And it's uncertain if a hastily scheduled new election would create a different result.
So attacks of Trump himself would only be justified if he knew about it, didn't alert the agencies responsible for the election or actively engaged in it. And quite some people in his inner circle have been indicted for that, while he himself engaged in pretty blatant obstruction of justice to prevent further investigation of those claims. So the claim would not be completely unsubstantiated (depending on how broad or narrow you allow those claims to be).
Also:
The 2016 election did end up being accepted by all reasonable experts eventually but are there examples where it was not and still remains hotly contested?
Is a pretty weird way of phrasing that Clinton conceded the very next day:
https://time.com/4564480/read-hillary-clintons-concession-speech-full-transcript/
And allegedly did so in private even before that.
