Did some more testing, apparently the inspire doesn't work on any character's melee or ranged single attack. Melee aoe attack works fine just like bursting fire.
Basically it's not the bursting fire is too OP, the bursting fire is working as intended while melee and single range attack is buggy as fuck.
I mean, burst fire is still OP, because of how it interacts with damage bonuses, +20 bonus applying on every shot in 12 round burst will be 240 extra dmg (realistically even more because it will be multiplied on crits), while for single attack it will be just 20.
Apart from bugfixes, imho they should really make it so conditional +damage bonuses apply only on the first shot, or are spread between all the shots in the burst, with only bonuses from things like weapon expert talents and specific heavy weapon talents, applying to every shot in the burst.