Lots of talk about "trust in elections" these days, some of which is defensible but has only very narrow application, and a lot of which is obvious nonsense. A few reminders:
(1) 'Public trust in elections' is not a magical quality adhering to election systems; indeed, it doesn't even concern any one particular thing, as all election systems have multiple working parts that have to come together. The only thing of any importance with regard to the term is whether people, as a whole or in large groups, think any concerns they have about illegalities are being at least fairly considered. There is one and only one way it can be undermined: by refusing to consider and address concerns that people have.
(2) Because of (1), the robustness of an election depends entirely on its welcoming any concerns people might have, for whatever reasons, and assessing them in as fair and impartial way as is possible. If your election system needs to be protected from people crying foul -- for whatever reason -- there are only two possibilities: either your election system is corrupt (and you are trying to protect its corruption from being exposed) or your entire society is on the verge of immediate and unavoidable collapse (and you are simply buying some time). There's not actually a third option here. An election system that cannot endure challenge, even extended challenge, is not robust and is already either corrupt or collapsing. The American election system is not even remotely in the vicinity of collapse at present; we haven't even finished counting the votes, all the problems so far are problems foreseen by statute or manageable by courts, and none of our constitutional back-up systems are even at present in danger of needing to be engaged. What is more, the American system is very, very robust; contrary to the way some of the chattering classes talk, we have recounts and litigations and accusations of unfair practices every single election, and the whole thing is still standing just fine. And the whole thing is still standing just fine because (unlike apparently some of the chattering class) elections are designed to weather these kinds of challenges, and this is how they establish their trustworthiness.
(3) Again, again, people, the American presidential election is a multistage election that has not been completed yet. It's inappropriate for presidential candidates to assume that they've won an election that isn't over, yes, but whether it's Trump claiming that Democrats are trying to steal the election he actually won or Biden flat-out lying about being President-elect of an election that literally can't have actually elected him yet, it isn't a 'threat to democracy'. It's not all in grave danger just because politicians play to their supporters with over-the-top rhetoric; it is, crass though it may be, exactly what one would expect them to do.
(4) Concessions are not a part of the actual election election process, for the obvious reason that it would be moronic to make voluntary concession a part of your election system. It was a polite courtesy that developed to show good sportsmanship and, eventually, a way to address one's supporters when it became clear that one had lost, and that is it. It is a campaign signaling a step down, and that is all. Whether a candidate concedes or not has no bearing on the election whatsoever; whether and when and how to concede is purely a matter of political calculation on the part of a campaign.
(5) Some people have been worrying about 'the transition'; this seems to me to be an example of how the chattering classes can talk themselves into irrational priorities. The transition serves the election, not the election the transition. Before the Electoral College votes, the statutory transition phase begins when the General Service Administrations recognizes a candidate as likely enough to be elected to be given certain administrative accommodations to facilitate the actual transition when the President takes office. As of yet, Biden has not been designated probably President-elect by the GSA, and it doesn't really matter what the reason is, because it doesn't really matter. Biden is an ordinary citizen until he takes office and is not entitled to anything; 'President-elect' is not an office of the United States, and the only constitutional responsibility a President-elect has is to show up to be sworn in. There are obvious reasons why it's convenient to start preparing for a transition as early as one can; the Office of President will not collapse if the transition period is shorter. A competent campaign will have most things ready to go in any situation that might arise, and if they don't, it doesn't affect anything but themselves.
People are, of course, perfectly free to complain about lack of courtesy, or lack of honesty, or lack of good will, or inconvenience, or the absurdity of some of the accusations, or what have you; there's certainly plenty to complain about in politics even in the best of times, and there surely is much to complain about here. But none of these things have much to do with trust in the election system, and none of them have any bearing on its course at all. People need to get a grip and stop jumping immediately to the most hysterical rhetoric they can; it makes them sound delusional. If there are any legal issues anyone wishes to raise, they need to be assessed and addressed, and it doesn't matter what grounds they raise them on; if people demand recounts and audits, it's not a threat to democracy to have recounts and audits; if people litigate, it's not a violation of 'democratic norms' for courts to assess whether officials actually followed election law as they were required to do; it's not a constitutional crisis that Trump refuses to concede, nor that Biden (like Trump and Obama before him) goes around claiming to be the occupant of the entirely fictional 'Office of the President-elect'; no matter how much states that are efficient are to be praised, it's not a problem that it takes a while sometimes to get the tally on votes, because the American election system has literally been designed to handle even worse and more controversial delays than this; and we still have two major steps in the election to go.
Part of the problem, of course, is that we all have difficulty dealing with the politics that actually is, which is tedious and boring and sometimes takes forever and takes some focus, and we all find it much easier to freak out about wild fantasies in our heads, whether about what we fantasize our opponents will do (no matter how many endless numbers of times our predictions fail), or about what our opponents are doing behind the scene (no matter how many times we show that we actually haven't the faintest clue what our opponents are actually thinking), or about that thing that Betty said Tom heard that Joe whispered had been evilly done. But our fantasies are irrelevant to how the election system is going, and it is still going, quite as it is supposed to, right down to the challenges that people have every right to bring if they think it will give them a fairer shake to do so. The election system is only strengthened by challenges, and it's not going to be toppled by opinions or rhetorical posturing, no matter how stupid you think the challenges or opinions or rhetorical posturing are.