I wonder, did you consider Al Gore as the elected President in 2000 prior to the results of the recount and EC vote?
Try a different angle. I stayed up until the wee hours that night, and went to bed after the networks declared George Bush the victor.
So, by some logic somewhere, Al Gore should have given up, because the networks said George Bush was the next President of the United States.
And yet, they kept counting, because networks don't declare presidents. The projection made by the networks is irrelevant.
So one might ask if I thought it was ok for Al Gore to keep fighting even after the networks declared George Bush the winner, shouldn't I say it is ok for Donald Trump to keep fighting even after the networks declared Joe Biden the winner?
In my opinion, it's ok for Donald Trump to keep fighting. The network declaration has no legal significance. However, what he does in that fight reflects on him, and could cause damage to the country. Al Gore didn't say there was massive fraud. Al Gore didn't declare that the election was rigged because of bad ballots. (And....George W. Bush did, in fact, win because of bad ballots.) Al Gore said let's play by the rules, exhaust our legal options and count every legal vote.
If that was all Donald Trump was saying, I think it would be just fine. Instead, he is accusing people of fraud, lying to the people, and undermining democracy. Demanding that we count every vote isn't undermining democracy, but demanding that we throw out votes is.
And of course there's another, purely practical, perspective. Al Gore had a legitimate possibility of being declared the winner. Donald Trump does not. His actions are just making a lot of people go to a lot of trouble that they don't need to do, except to satisfy the whims of Trump. He lost. Nothing is going to change that. I don't know exactly what the Secretary of State does every day, but I'm guessing that they would be doing something at least somewhat worthwhile if he weren't getting ready to count five million votes by hand. Trump should let people get on with their work. He has a legal right to try every legal avenue, but it's completely futile, and embarrassing.
It does have one positive effect though. There are people who voted for him, and this display will help a small number of those people realize why so many of us despise him so much more intensely than we despise other Republicans.