VP storyline didn't follow the constitution

As much as the characters like to talk about their reverence for the constitution, the show did not seem to follow it at the end of season 7.

The VP candidate died the day of the election and the ticket won the most electoral votes, leading to the problem of who becomes the VP. The show depicts the choice as between the president-elect and party telling the electors who to vote for vs. going into office without a VP and then appointing one via the 25th amendment. The show posits the second as the choice with more integrity and so that is what they do, because, I guess, the characters in the show must always be doing something heroic every episode, unless it's a long arc about how they slip into error for a while so that they can be more heroic later.

In real life things would probably have gone a little differently:
1. The electors have the responsibility for their vote. They can listen to the president-elect or the party, but are not required to vote the way that they want to. There are a lot of unexplored possibilities here. They might even have gotten together and talked with one another about whom they preferred.
2. There is still a vote, not shown in the show at all. Someone might well have been elected VP at this point.
3. If no one got a majority in this vote, the matter goes to the Senate, with the top three vote getters all being candidates. If no one gets a majority on the first vote, they keep voting until someone does get a majority. Since the Senate was probably dominated by the other party, they would probably have elected a Republican. So it would behoove the Democratic electors to have elected one of their own back in step (2).

The 25th amendment would not have come into it at all. The show is presenting a false premise there.

Even the characters' analysis of the false premise seems dubious. They claim that the problem is that one person is picking the VP without the approval of the people. However, if the VP candidate had lived, wasn't that pretty much the case anyway? One person, the presidential candidate picked the VP candidate. The voters voted for the ticket, but almost none of them cared who the VP candidate was. Every election shows that only the top of the ticket actually matters. So really there's almost no difference.