So you need something around 5 players full equip, with mech and T4 armor, weapows and ammo. To get 3 heart so you can spend a lot more resource to do 1 pragmium hatchet and than you can get 250 of wood with 1 axe. Looks very reasonable to me

What ? No , have you even slain the queen?
You dont need t4 armor as you dont need to leave your mech.
It can be done with 3 players but your mechs will take a beating
With 5 players you lose roughly 200 bullets (.300 ap) and 25 to 50 percent mech armor.
Pretty much the gold you earn from the fight goes back in to repairs.
In total each queen fight drops 16 hearts. 1 heart makes 1 harchet.
Also i think like total approx 150 prag and 130 gold. In addition shooting the queen gives loads of LP and killing her results in 100 LP bonus. Actually just standing in the crater even without engaging give you 100 LP.
Maybe it needs some slight buffs but its not terribly unbalanced. I personally think the hatchets are fine i have 15 in my inventory right now.
I would prefer the gold drop to increase so that you actually earn some gold rather than break even. Give a good amount of gold would be a great constant motivation to battle queen.