If you subtract a dark frame you are ADDING more random (thermal) noise, just as much as if you add a real data frame to the stack. If you add enough frames the random noise eventually smoothes out, and this happens whether they are dark frames or data frames. But with dark frames you are adding only noise, not signal. Therefore it is better to stack as many real data frames as you can. There is no problem using 100 data frames! Mechanical shutters in DSLRs are rated at well over 100,000 operations (MTBF) and in compact cameras the “shutter” is electronic and so should have no practical limit (something else will fail first).
So the key is to use MANY exposures and appropriate stacking software. (Fixed-pattern noise and bad pixels are smoothed out by the fact that images taken on fixed tripods or unguided EQ mounts are all shifted in relation to each other, which the stacking process addresses.)
As to the idea that you cannot use bottom-of-the-range cameras, that is also wrong.