I can see good arguments for the President having immunity for things done during his term that are connected to his duties. I can see good arguments for delaying prosecution until end of term while he's in office. I can't see any good arguments for the President having immunity for things done outside his term as President being prosecuted outside said term, or things done during his term but unrelated to his duties being prosecuted after said term.
It's not like you can just accidentally the whole felony.
This is an interesting one. Imagine an executive of a company committed a crime as part of company business, or directed his company to commit a crime. What would we do then? I think there would be significant dissatisfaction if they had "immunity", and only the company could be penalised. Nevertheless, I would perhaps agree and lean to the idea that the complexity of government means that a certain level of immunity for work "connected to his duties" is the most practical option. However, the key issue then that needs to be addressed is where, precisely, "connected to his duties" ends.
My feeling about SCOTUS here is they simply want to de facto absent themselves. We started off with the majority decision argument on the insurrection case, which was to claim that a president would only be barred by an active vote by Congress, rather than a bar automatically applying if a relevant conviction was secured. Sure, this is a very dubious argument given apparent wording of the Constitution, but in the end, their word is law so why do they care?
Then all the other cases, the conservative justices appear to me to be delaying, or crippling, the cases. I think not because they're protecting Trump per se, but because
they don't want the courts to deal with it. They want to protect themselves from suspicions that they could play as kingmakers, interfere in democratic process. Trump might be as guilty as sin, but as far as they are concerned that's the business of Congress to deal with: it's got the tools and should use them. Even if outrageous to halt the cases outright, subtly sabotaging them means the prosecutions fail and that suits them fine. If delayed until after the election that is great, because it takes the electoral interference annoyance away from them. The fact that it means a man who has potentially committed crimes is left free to assume the presidency (and by extension presumably others in the future) is a triviality. Nor do they feel there is any pressing need or democratic value for voters to know whether a candidate accused of crimes has committed them. If this makes presidents de facto immune because deadlocked Congress will nearly always mean no-one can be successfully convicted in impeachment, that's just up to Congress and the voters to dwell on. That is how they want it in order to protect themselves and their institution.