That's not exactly what happened in Florida 24 years ago.
In principle I don't really disagree, but just saying the problems run rather deeper than just hand-counting vs. electronic voting. The one time a recount actually would have been useful it was stopped for highly legalistic reasons that are hard to explain to a normal person. Not only that, it's highly likely – perhaps even probable – that Gore won Florida, although we'll never know for sure.
I see no reason it would play out any different today. We all saw what happened during the last election.
Not only that, with the full-on cult of Trump and the perceived victimhood of his supporters, I'm not really sure to what degree hand counts can always be trusted. Given the very small margins in some states, even a very small error rate (malicious or otherwise) can really matter. Perhaps this is paranoid, but I fully expect Trumpdroids to try to cheat. Any idiot can cheat a handcount "by accident" (prove it otherwise), but actually tampering with voting machines is operationally much more complex, and not something any ol' yahoo can easily pull off (need not just technical knowledge, but also physical access).
tl;dr: it's all pretty fucked no matter what.