Maybe I made a calculation error, but a flamethrower that can shoot flames higher than most mechs are tall doesnt seem right.
Whereas building the mech in the first place makes perfect sense?
This is fantasy engineering, after all.
Your calculations are correct. It seems reasonable to me. Achieving that 125-foot flamethrower requires 6 steam powers, or all the steam powers of a normal 5th level coglayer. A coglayer with a higher Int and the right feats could build this weapon sooner, but it would still constitute a healthy portion of his total power output. Meanwhile, wizards of similar level are lobbing around 2nd or 3rd level spells, and fighters are learning Great Cleave.