Yep. I always thought it should be different. The boss takes more damage sure, but instead of becoming easier, they should fight harder instead to compensate for the extra damage they are taking.
It's a good thought, but fighting harder would level out the advantage that the weapon is supposed to provide. Earning a weapon and figuring out boss weaknesses should be rewarding, but not if just makes the standard Buster the safer option for the next boss.
If anything, baseline boss difficulty could be tweaked. Maybe faster movement/projectile speed, or more damage. One of things about older Megaman games is that many bosses are exceedingly brutal with the Mega Buster alone, and the weapons you gain are intended to compensate for that.