I consider Augmented Engines (and Unstable Injector if I do not have AE) so game-changing that it goes on every ship (except Ox and any other ship with too few OP to use AE). However, sometimes in food runs, I need as much cargo capacity as possible, and strip AE off of 20+ ships to get maximum cargo space. Once I make it to my destination, I cycle through those same 20+ ships and restore AE. Earlier in the game, when scraping after cash, I have stripped AE after combat to take more loot, even metal (because metal can be worth lots in disrupted markets); then restore AE after I unload.
I think all ships' top speed to be raised across the board and Augmented Engines should just give +1 burn and maybe +5 to top speed. Unstable Injector could just be a degraded hullmod for extra-fragile engines on enemy ships that need it like in A Fistful of Credits, and Auxiliary Thrusters can inherit the acceleration from Unstable Injector.
Related: I consider Dedicated Targeting Core/Integrated Targeting Unit so important that it too goes on almost every warship, with few exceptions. Few ships, like Gemini, have few enough OP that it cannot afford ITU. Ships that use nothing but missiles, so as torpedo Mercury or Afflictor, do not need ITU, and civilians that are hopeless in combat do not need it either.
Correction: I do not use Augmented Engines on Hyperion. It does not need it in combat (because it teleports), and as a frigate, has high enough burn without Augmented Engines.