My take on those points:
Friendly fire: meh, fireball staff is far worse. Getting tapped by beam doesn’t hurt that much unless they are really trying to hit you. Randomly getting singed by a fireball staff can knock off 10hp a pop. For that matter, a careless bounty hunter will hurt you a lot more than a beam sienna.
Easy access to a crit exploit: There are plenty of “exploits” that end up being core mechanics of a given game. Simply calling it an exploit isn’t enough to prove that it should go away.
Don’t need a weapon: There are plenty of builds that can do just fine with one weapon as long as they are supported properly, and a pyro that mispositions and gets surrounded is not going to do very well unless she switches to melee.
Kills chaos warriors fast: dual daggers can 3 shot chaos warriors without using a cooldown at all. Chaos warriors are a pain with most weapons, but this is far from the only build that can shred them. It may be the best build against them, but I’m not convinced that it should be nerfed because of that.
It can still clear elites and specials: dd/hagbane waystalker has great waveclear, great boss dps, and can handle elites/specials just fine. BH and huntsman don’t have quite the same level of waveclear, but they are arguably better against elites and specials.
It outclasses other builds: I’m not convinced of this at all. It outdamages a lot of builds, yes. If you position really well, that means that it outclasses a lot of builds. If you mess up your positioning or miss a special, you sort of just die, when some of those builds you “outclassed” would remain standing. In practice, if an average player is trying to maximize their legend quick play winrate, I don’t think that any form of pyro is the best option. It might be a good option for an elite player trying to speedrun maps, but I don’t think it is actually the best option there either (mostly because of the lack of mobility). It definitely is one of the best options for getting green circles in winning runs, but I don’t think that that is a useful metric.
Friendly fire again: see above
Ammo: yup, waystalker/bounty hunter/huntsman/ranger veteran are all well known for being short range or running out of ammo regularly.
See it a lot: fair enough. I don’t notice it enough to bother me, but to each their own.