Angel doesn't need to be a vampire to be a hero. He will still be the imposing, ballsy, fearless guy who bursts into rooms and breaks faces off his fists. He will still have over 250 years of experience of life, the supernatural and fighting. He will still try and do good works to the best of his abilities. He will still feel guilt for all he has done wrong. He'll still wear and black and sadly, he will still like Barry Manilow.
Being a vampire is not the sum of Angel. It is merely a part.
If he can adapt to having a soul, he can adapt to having a heartbeat.
But my point is, Angel WON'T be that "imposing, ballsy, fearless guy" anymore. As a human, he will be far less imposing, and common logic would dictate that, if he has any sanity at all, he will most certainly feel fear any time that he would confront things that, as a vampire, would have been little more than a nuisance. Fear is a common human trait. It can be accepted and worked past, but the fear always remains. Angel's two and a half centuries of experience may still be there, but any experience that he might have gained in fighting will be next to useless, because it is based on fighting with a level of strength, speed, and endurance that he no longer has. The fact is, as a human, Angel will have little or no more fighting experience than Xander, and most certainly less than Gunn or Riley. At the very best, or maybe worst, he will have the attitude of someone who was, literally, one of the four greatest fighters in the Buffyverse, but he simply won't have the ability to back up the experience. Visualize Angel trying to beat someone like Hamilton as a human, when he barely managed it as a vampire.
As a human, Angel would have to learn how to fight, or even survive in the supernatural world, all over again, just like Spike had to do while adjusting to the limitations imposed by his chip. Visualize Riley, crashing into an unchipped Spike's crypt and slamming him against a wall, or even throwing him out of Buffy's house. It took Spike months to first accept, and then adjust to the limitations of his new existence, and all that he had to adjust to was the fact that he could no longer fight or harm humans. Angel would have a far more difficult time learning how to fight demons whose power, relative to his own, would be far greater than Hamilton's ever was, and feeding off of their blood wouldn't do anything more than give him an upset stomach.
I'm in no way trying to say that Angel wouldn't want and try to continue to fight, I'm just saying that in order to do so with any agree of effectiveness, he is going to have to learn how to continue that fight with all of the limitations that any other human would have, and gaining the skill necessary to do that is going to take months, if not years. Add to that the fact that even once he masters that skill, he will never, ever, be able to be the fighter that he once was. How hard is that going to be. How is he going to react the first time that Buffy or Faith have to bail him out of a situation that he could have easily handled a year ago. How is he going to feel when Spike has to rescue him?
Becoming human is the end of Angel's quest, but in order to complete that quest, even if he ever is capable of doing so, will tale all of the strength, skill, and determination that he, as a vampire, can provide. Without that power, he simply won't be able to do it. And HE has to do it, alone, without relying on help from anyone else.