Lots of mutations occur as an accident. The harmful ones die out quickly, the helpful ones get spread, and the ones that people specially select will become common in captive chickens.
Things like crest, muff/beard, silkie feathers, and frizzle feathers would all be disadvantages in wild chickens. But people like them, so the people keep breeding them.
The pea comb mutation happened at some point, and some people kept breeding it, so it is still around in domestic chickens.
People in cold climates have been more likely to select for pea combs, but they are also more likely to select for chickens with large amounts of feathers (like Brahmas and Orpingtons.) To see if pea comb is a problem in hot weather, I would look at pea comb chickens from hotter places (examples: Cubalaya, Sumatra, Aseel). I would also look at some of the Easter Eggers that have large amounts of Leghorn in their heritage (example: Whiting True Blue from McMurray hatchery.) That should make it a comb difference only, not a comb + feathers difference.
Your point about cockfighters removing single combs (dubbing) is interesting, because some of them are in hot places. If the dubbed birds fare poorly and the un-dubbed birds are fine, it would be pretty good evidence that comb type matters in the heat. If all the birds do equally well, it would strongly suggest that a small comb (dubbed or pea) is just as good as a normal single comb in hot weather.
I have never lived in a place that gets very hot, so I don't have any personal observations of pea comb vs. single comb chickens in hot places.
I know of at least three points against pea combs:
--Pea combs are smaller, so it is harder for people to recognize male chicks when they are young. This does not hurt the chicken, but is a point that matters to some people. (I read of one breed-in-development that has single combs for exactly this reason.)
--The pea comb gene also causes a strip along the breastbone that has no feathers. This does not seem to bother the chicken, but does affect how it looks after butchering (different texture to the skin there.) This matters to some people raising chickens for meat (especially commercial meat-producers.) I can't remember whether this happens only in chickens homozygous (pure) for pea comb, or if it happens in the heterozygotes (split) as well.
--I have noticed that roosters seem more attracted to hens with single combs rather than pea combs, probably because the single comb is larger and more obvious. Roosters tend to mate with the laying hens (big red combs) and not with immature pullets (small combs). If the rooster considers the pea comb hens to be less desireable, this could potentially be an issue in a flock with mixed comb types. In practice, it does not seem to be a big deal in most flocks, because most roosters end up mating with all the hens often enough and with their favorite hens more often than that. I would not expect it to be a problem in flocks with only pea combs.
Personally, I like pea combs better than any other comb type, and I do not see them causing harm to chickens (but I'm not in a very hot climate). But any person can have different preferences about what comb looks best to them, and the points I listed can be important to some people.