I was watching the Biden/Trump Presidential debate and it was quite difficult to follow due to candidates speaking out of turn and constantly interrupting each other. Why don't these debates simply disconnect the candidate's microphone when it's not turn to speak, to make it impossible to interject out of turn? Has this been previously considered?
Just a theory: previous Presidential debates were conducted with greater civility, and that civility functioned as a sort of automatic inner software mute switch that was already installed (via education) in the conscience of each candidate. There were occasional interjections now and then, but not enough to impede the general flow of the Presidential debate format.
So there was never before a need for a hardware mute switch... until the format met with a candidate without that software mute switch.
It's been done before. It comes off as unfair.
Generally the Commission on Presidential Debates tries to keep impartiality, and turning off a candidate's microphone looks like you're favoring their opponent.
Not that this would necessarily hurt the person whose microphone was turned off. In Reagan's case, this actually helped him and was even credited by some for giving him the White House (emphasis mine):
On February 23, 1980, the Telegraph received national attention during the New Hampshire presidential primary, when it hosted a Republican debate paid for by the campaign of former California Governor Ronald Reagan. During a discussion over which candidates should be allowed to participate, Telegraph editor Jon Breen (1935-2017), acting as moderator, ordered sound man Bob Molloy to shut off Reagan's microphone, which was met with shouts of protest from the audience; Molloy refused to comply.  Mispronouncing his name, Reagan rebuked Breen saying, "I am paying for this microphone, Mr. Green!" [sic], which was cheered by the audience and applauded by most of his fellow opponents. The phrase entered the political lexicon and the publicity helped to boost Reagan's successful run for the presidency.
Reagan later recounted the incident as a "brief and seemingly small event, one lasting only a few seconds", that he said he thought, "helped take me to the White House".
After reading some comments, I have decided to expand my answer slightly and address probably the biggest criticism to my answer.
Some have pointed out that this could be implemented fairly. And I wholeheartedly agree that this could be implemented fairly.
The key here is that to do it fairly, it must be agreed upon ahead of time--which it was not in this case. Just doing it on the fly and just saying, "Hey, sound guy, turn off his mic!" comes off as unfair.
Interestingly enough, since this question (and answer) was originally posted, the Commission on Presidential Debates has now come out and said that they want to add "more structure" to the debates:
The commission said Wednesday the debate “made clear that additional structure should be added to the format of the remaining debates to ensure a more orderly discussion of the issues.”
One such option discussed is exactly this:
One possibility being discussed is to give the moderator the ability to cut off the microphone of one of the debate participants while his opponent is talking, according to a person familiar with the deliberations who was not authorized to discuss the matter publicly and spoke on condition of anonymity.
Though, worth noting is that this last piece of information comes from an anonymous source and not directly from the commission itself.
People don't want to see a series of speeches, because yawn.
They want debate. They want the cut and thrust, and that means interjections and interruptions. They want to see the politicians being challenged by each other, to see the candidates remain calm under fire. They also want the candidates to have the ability to fail by making too many unnecessary interruptions. They want the candidates to be able to make gaffes and demonstrate personal weakness in civil debate.
So I'm sure that if it was considered as a general principle, it was quickly discarded as being counter to the purpose of the show, which is to get the candidates to lock horns and see if one can out-argue the other.
And if it is done responsively (to silence a candidate whose interruptions are excessive) it looks unfair, and may be unfair.
In the recent debate, it seems that Trump was using interruptions as a deliberate tactic: to get Biden flustered and angry, as an angry person may make gaffes or misspeak. It is up to voters to decide if this succeeded.
Ideally, they would be respectful and mature enough that such measures would not be needed. Preferably, there would be precedent for polite, constructive argument exclusively on your turn to be the norm, and a certain amount of shame would be placed upon people who break that precedent. It is debatable whether such precedent exists, and given how the senate and the house of representatives operate, I'm inclined to believe it doesn't. However, in this debate, the precedent, whether it is for this style of debate or something more like I described, does not matter.
I don't think it is too political to either side to point out that the incumbent's main selling point is that he has very little shame, if any. Whether such a precedent exists is therefore irrelevant, since it works best to his strengths to ignore it regardless. He garners the most favor when he does exactly as he did here, militant interruption, making sure he is the last word, and saying whatever he has to to make the conversation steer towards where he wants it, even if it doesn't make that much sense in hindsight. The power in this strategy is that it completely shuts down every other strategy, since if no one else uses it or something similar then their speeches and posturing never reach the audience, as they keep getting stepped on, metaphorically.
A judge or regulating body given the right to silence all but one speaker is another way to make such debates more fair, mostly regardless of the respectfulness and maturity. The assumption would be that that judge was given that power by the candidates, and they are giving the judge the right to silence them, since that is what is most fair, and barring that, it is what is expected of them. You will note that this is the method implemented here, and in all presidential debates I can remember, but Chris Wallace's power in this debate is simply not respected, because the incumbent's strategy does NOT benefit from doing so. Therefore, the other candidate is under pressure to also not respect his authority, though you may note he tried to do so for a while.
Why not disconnect the other microphones?
Cutting the microphone signal would stop the out-of-turn candidate(s) from being heard directly by the audience (though they may still be heard coming through various other microphones on the stage). This would not prevent the other debate participants from hearing the voice of the person interrupting.
Turning off the out-of-turn microphone(s) would then require the in-turn participant to make their response without being distracted by the out-of-turn comments. If the in-turn participant is distracted by the out-of-turn comments, they risk portraying themselves as unfocused at best and possibly even senile. Conversely, a particularly adept participant may attempt to put words in the out-of-turn participant(s) mouth by responding to comments which were never actually made.
Having the out-of-turn microphone(s) on allows for the audience to hear the distractions as well, putting any reactions from the in-turn participant into perspective. It also gives the in-turn participant the opportunity to spin the optics of the debate if they are capable of managing the overall tone of the interruptions with their ability to respond.
Has this been previously considered?
Yes. I'm sure virtually anyone who has watched a heated debate has asked this question. Those administering and participating in the debate must surely have considered this at some point and have therefore made the considered decision to keep all microphones hot. There is currently and has been conversation about muting the other microphones, but it has not been common practice in debates.