> It's either resistant or it's not.Resistance is not a binary thing. Often it simply means that a population of "resistant" bacteria takes longer to be completely eliminated, not that they are completely unaffected.
It would be better if a different term were used to describe bacteria that are completely unaffected by a given antibiotic; perhaps "invulnerable" would do. If you are in fact dealing with bacteria that are invulnerable to a particular antibiotic, then you need to switch antibiotics, yes.
> Bacteria multiply far far too fast for them to notice multi-day courses of treatment
Bacteria multiply far too fast under ideal conditions. But the whole point of giving an antibiotic is to make the conditions as far as possible from ideal.
> a bacteria only "notices" the current conditions before it either multiplies or dies
Bacteria are not mayflies. They don't have to either multiply or die within a short period of time.
> It seems to me that instead we should use just enough antibiotic to keep the patient alive (to turn the corner) and then let the patients immune system do the rest.
Antibiotics suppress the patient's immune system, so once you have started them, you need to finish the job with them.
If you are going to try to let the patient's immune system fight the infection, then I would think you would not give antibiotics at all; instead you would focus on maximizing supportive care for the patient's immune system (for example, they probably need to eat a lot of protein since the immune system needs protein to make antibodies, T-cells, etc.), and for the patient generally (make sure they stay hydrated, etc.).