I think we have a real problem in the public's perception of election integrity. So statements by the election official that "we can do whatever we want" because "precedents don't matter" shakes the public's faith in the system and the people who run it. There need to be clear standards for voting and you should have your ballot in to be counted by election day. We've got to end this counting one and two weeks after election day.
I don't disagree with the criticism of that particular election official's statement, but the principal reason there is any issue with the "public's perception of election integrity" is because conservatives have been claiming in bad faith, without any evidence, for years, that there is pervasive voter fraud directed against them. These constant baseless claims of voter fraud have served the purpose that was intended by the conservatives who made those statements (and also the foreign actors who have pushed those narratives), which was to undermine voter confidence in elections. In essence, conservatives have intentionally created this distrust in hopes that they can leverage it for their own purposes.
As for the rest of your post, most of the confusion about "standards for voting" and how long it takes to count votes is because every state is in charge of its own voting procedures, per the Constitution. Most of those voting laws have been in place for a long time and are not well understood by people, which leads to criticisms that are not based in reality. For example, Charlie Kirk was posting on Twitter about Democrats trying to "steal" the NC Supreme Court seat because they are still "counting ballots" in North Carolina. What they were referring to were the county canvasses, which occurred this past Friday in accordance with state law. The county canvasses are where the county election boards resolve disputes over whether particular votes should count, determine whether to count provisional ballots (state law provides a number of scenarios in which provisional ballots may be cast), and count late-arriving ballots from overseas military members (by state law, such ballots can be counted if received up to the day before the canvass). There was nothing remotely improper happening at all; they were just following NC state law (and as you know, NC is a state where the legislature has been controlled by Republicans for over a decade now).
Having all ballots counted by election night is the kind of thing that sounds easy and simple in principle but likely doesn't work all that well in practice. At the very least, there is no time to resolve any challenges over disputed or provisional ballots. And because everyone recognizes that having voting machines hooked up to the internet is dangerous, you still have a system that relies on getting a lot of information from a lot of different precincts related to the election, especially in larger states. And that is not even accounting for the fact that sometimes things will go wrong - voting machines will break, etc.
