I do respect him and his achievements and he is great for tennis. I just don't agree with the narrative that he is the greatest of all time. I also never understood why it was never to be challenged when Rafa and Djoker were coming up behind him posing some serious questions.
To answer your question, no, of course not only ATG's count as competition but the level that Fed had to beat two win his slams up until the emergence of Djokodal was much lower. Once these guys showed up they started causing him a lot of problems and the winning rate slowed dramatically. At that was when he was still only 27.
I don't believe he's the GOAT, but he is the most successful singles player to date because of his 20 GS, and he's earned that. As things stand, the GS rankings are still 20-18-15 - if that's still the widely accepted main metric for people to consider someone as GOAT, I don't see why it's unreasonable for people to
argue that he's the GOAT, or that he has the
best claim to be GOAT, at least currently. Should Nadal and Djokovic get to 20, things get muddier, as they should. If they get beyond 20, then they should have the better claim to GOAT.
His winning rate slowed dramatically, because not only are Djokovic and Nadal tier 1 ATG's themselves, they're significantly younger too. I don't think Federer could have done much better than he did, considering how strong Djokovic and Nadal were and still are. If Federer's position was reversed, with Nadal or Djokovic being older, I don't think they would have done any better. That's of course an untestable claim, and therefore irrelevant.
Federer always had issues with Nadal, but I don't think it was because Nadal was a completely superior tennis player. He had matchup issues, and that he never overcame them until much later is to his discredit. Nadal, after all, beat peak Fed in Wimbledon 2008 and AO 2009, and was beating him on hard courts from the start. With Djokovic, I think the age gap really played into his advantage. Fed led the Slam h2h with Djokovic until their 2014 Wimbledon match, when Fed was already 33. He went 2-3 in slams vs a beastly Djokovic from 2011-2012. I think Djokovic and Nadal make him look a lot worse than he really is because they've had the opportunity to abuse the age gap, especially since Fed ended up playing for so long. IMO, the 3 of them are very VERY close in overall ability, and it's too difficult at this point to claim one as clearly superior.