It's important to remember that Bush was strongly opposed to a full statewide manual count. Republicans were arguing that it would be too expensive and too arbitrary. Ultimately the Supreme Court ruled against a full statewide manual count, IIRC.
I definitely agree that there should have been one, but it's wrong to put all the blame on Gore. Both sides were willing to do whatever it took to win at that point. That doesn't excuse anyone's behavior or make it right, but it's the facts and the reality of the way politics works.
Gore didn't ask for a statewide recount, at least at the beginning. He ask for recounts in areas he thought he would do well in, but it turned out that he
lost votes in those. I suspect that his real intent, later was to delay the count and say, "Well, Florida waited too long to cast its votes, so I win."