Overdrive is helpful, yeah, but as a game mechanic it’s pretty unimaginative since it doesn’t really trade anything substantial for the massive dps boost you get. It definitely needs changes; the concept of a temporary boost has merit but it needs to have its drawbacks so that you just don’t spam it every time. I completely agree that merely overheating faster isn’t enough of a detriment since you still save a lot of time with it. The matter was discussed here previously, feel free to check that out.
However, the focal point of your complaint- that of bosses dying far too fast is linked to a bigger problem, with that being the severely steep difficulty curve this game has. I assume you were playing on lower difficulties, since it takes a few seconds to dispatch of bosses on lower difficulties, however higher difficulties are much, much tankier, and take a while to finish, even with Overdrive. This creates a paradoxical situaution such that it’s impossible to do harder difficulties now without it, but on the other hand easier difficulties are cheesed too easily. Bosses dying too fast has been somewhat of a problem since the weapons were reworked- for some reason higher difficulties got buffed more and more, with easier difficulties not being scaled appropriately; resulting in an extremely steep difficulty curve. The existence of Overdrive is only one of the many reasons bosses are unbalanced in the game currently, and that problem needs some attention from iA.