States run elections. Even if Biden were do try to prevent trump from appearing on the ballot, the states doesnt have to obey, especially if the supreme court's decision is contrary to the president's orders. And if trump appears on ballots, throwing him in prison wont do any good since if elected, as he did in our timeline, he becomes president on January 20th and can order the military to break him out of prison, whether state or federal prison.
And if the states somehow prevented trump from appearing on ballots, we'd be in a constitutional crisis and also a state vs federal government political crisis. Pro trump supporters will cite the supreme court decision as a rallying call to trump supporters around the country to protest, and use violence if necesary.
Well you might say, who cares what his supporters have to say. But the point is if the 14th amendment has a more clear procedures of how to invoke the part about insurrectionists being inelibible. trump could be barred from office and the prorests would've been minimal since the media would portay it as more legitimate. But unfortunately, the 14th amendment is so vague that the supreme court decision would paint a different picture in the media and in public opinion, making it seem like Biden is being tyrannical.
Lol they can bypass the vice president ineligibility part by chosing trump as speaker of the house and then run placeholder candidates for president and vice president, then get rid of them and trump becomes acting president for the rest of the term.