For a Pyromancer, Chaos and Dark infusions are very handy, and best, obviously if you just buff your weapon with Carthus Flame you will deal more damage, but using Chaos or Dark infusions come very handy, you don't need to use a slot for Carthus Flame Arc, you don't have to rebuff your weapon everytime, you don't spend time buffing your weapon(and specially in PvP and boss fights you may not have time to do buff), you don't need FP to buff your weapon.
Also many weapons have really good scaling with Chaos or Dark infusions(both infusions always have same scaling):
A/A scaling for Carthus Curved Greatsword, Astora Greatsword, Murakumo, Great Corvian Scythe, etc.
B/B scaling for Carthus Curved Sword, Zweihander, Dark Sword, Claymore, Gotthard Twinswords, Greatsword, Cathedral Knight Greatsword, Lothric Knight Greatsword, Exile Greatsword, Onikiri and Ubadachi, etc.
These are just some examples there is a lot more good weapon with A/A or B/B scaling, and a few "meta" weapons with C/C scaling. As a note, if you know any weapon that scales S with Lightning or Crystal, this means it will have A/A for Chaos or Dark, if it has A instead of S then it will be B/B, and etc.