I . . . don't think Heavy/Assault 'Mechs are cheaper in the long run, unless you're using them to stomp the same enemies you would in Light/Medium 'Mechs. Heavy 'Mehcs facing other Heavy 'Mechs are going to take a lot more punishment and lose more parts, which should also be factored in. These 'Mechs are more likely to probably have a penchant for having ammo bins explode, save for the ones who strip it out. Honestly, based on tabletop and other experiences? You'll only get off easy if you're going after low-difficulty missions before Heavy or Assault 'Mechs (and vehicles) start making regular appearances.
And even then, "easy" is only one round away from "what the hell, why is the Thunderbolt on the ground?" if things align exactly wrong.
But this is false equivalence.
Facing heavy mechs - heavy/assaults will suffer more damage, true.. but the same is true for lights/mediums. And if damage suffered will be enough to crit ammo bins on a heavy - imagine what it would do to medium/light. Oh, and the kicker? Fixing structure on all mechs seems to cost the same. So still - damage that will tear off a limb from heavy would probably mean rebuilding a med/light from grounds up.
The incentive to bringing heavy mechs is always moar firepower, not the lower running costs which are counter-intuitive, to say the least. You want bigger toys? Pay bigger money and take bigger missions to pay for them.