I think I may be one of those people saying Pyro is better, I’ve said that several times on Steam. I made my own post just a couple hours before you did: Unchained Needs Love
You have some good ideas here, especially Enfeebling Flames.
Regarding Pyro being better at melee, it absolutely is. Pyro gets: 20% attack speed bonus, 50% crit chance bonus, and full uptime with no penalties (no chance of overload, no slowdown with Volans Doctrine). You never have to pull back on the heat to manage risk, just stay hot 100% of the time. Peak damage may be slightly lower (50% crit < 60% base damage), but uptime on the heat bonus is so much higher that Pyro easily exceeds UC damage totals by the end of a map. Also the benefits of a crit build (armor penetration on crits, Swift Slaying uptime) add up to negate whatever baseline numerical advantage UC has. Crunching the numbers says they are comparable, but in live gameplay Pyro is miles ahead.
PS, pls don’t nerf Pyro, it’s fine. It’s not OP or anything, in fact it’s still second fiddle to Battle Wizard. It’s UC that needs buffed. Pyro should be the baseline for the other two.