Queen doesn't impact Wildfire, it has been tested. You can also test it by throwing Wildfire to a dummy and summon the queen to do damage.
You'll be welcomed with a nice "0".
But the main problem with Wildfire is the lack of interactions.
For example during HW/SB, you have to prepare a wombo combo for Wildfire.
Today, Wildfire is a delayed 1200 potency skill, nothing else at it has no interaction, you only place it, press Hypercharge and continue your rotation.
Summoning a fire-spitting turret/automaton would be an okay idea. I don't like it because we would still have no interaction over the flamethrower but it's better than current Flamethrower.
Having one shared cooldown is not a problem. It's interesting on cooldowns.
The problem is that both are 20s cooldown and Bio Blaster isn't as impactful on a lone target. (60 + (60*5)) * Targets, on a lone target it's a weak 360 potency. On two targets, 720 potency, barely better than Drill.
The problem would remain the same, if not worse.
Battery gauge is designed to be flexible, at any battery spent you have the same damages overrall. Overcharging it to 120 would remove that flexibility. And you'd say goodbye to Queen during every Trick Attacks.
Plus, it wouldn't correct the Automaton that feels like a glorified dot.
With the heat gauge transfer, you worsen the state of the glorified dot. You make the queen a more glorified dot and your heat gauge is also a glorified dot!
I really don't like this idea as you loose more and more interactions. I don't want the job to play itself.
The main problem with MCH is that you're limited to 1 2 3, Drill, Air Anchor, DR/Ricochet, Summon Queen and Hypercharge (Including WF into Hypercharges) phases when it comes to damage.
Sam, for exemple has 3 different combo, Midare, Tsubamegaeshi, Sen'ei, Shôha, Shinten, Seigan and it's still one of the easiest Melee DPS.
Combo is uninteresting, there's too few cooldowns and little to no utility. It's the void compared to SB/HW utility.