There's nothing wrong with a long, drawn-out fight through the proper channels. A couple of months is not really a long, drawn-out fight by the standards of the American legal system anyway. Gore owed it to everyone who voted for him to fight for his win to the full extent of the law, which he did. When that was exhausted, he stepped aside and stepped out of the public eye for a long time. He did not push beyond the limits of the law, he did not rally his supporters against the new administration, he did not immediately start running for the 2004 nomination. When he finally did start making news again, it was, as you said, 6 years later. Bush had already been reelected with no interference from Gore. He didn't reopen any wounds, "An Inconvenient Truth" was not a political statement, it was not a diatribe against his political foes, it was not a platform on which to build another run for president. It was a return to the core issues that drove him earlier in his career. Issues that should be non-political in the first place.

To say "Gore is better than Trump on this" is to imply that they are both operating in the same universe, just on different levels. That is a false premise. There can be no comparison here.