I think you are right they would have ridiculous amounts of energy like you say, to be able to cross space between stars. I don't think that's as much a penalty

I think you are right they would have ridiculous amounts of energy like you say, to be able to cross space between stars. I don't think that's as much a penalty to detection as you, however. If you have an infinite energy budget, you could easily remove all the heat from the front of your ship via a Peltier cooler and radiate it out the back, for example. Then point your ship at Earth and you are stealthed from heat detection. Not all ships are merchant ships designed to get where they are going as efficiently as possible, after all. Some are designed to get somewhere as quietly as possible.