PWM speed controller with rectifier as voltage regulator?
No you can't. You need an inductor, which 'reduces' your idea to the well-known concept of a switched regulator.

The problem with your idea is that there is some resistance in the path between your power source and the capacitor, and this resistance will dissipate the heat that would otheriwse be dissipated by the linear element (pass transistor or the like). Switching does not help. An indiductor does help, because it stores the energy (and lateron releases it) instead of dissipating it.

Just in case you wonder (as I did long long ago): reducing the resistance does not help. You can prove mathematically that as the resistance approaches 0 the problem stays the same. An no, you can not get it to be zero, which is just as well, because then the current would become infinte, which (at the very least) would give 'interesting' magnetic effects.

Using PWM to deliver a 'reduced' power or as an Digital-to-Analog converter works only when you either


smooth the PWM output with a filter (you can use a simple firts-order RC if dissipation and bandwith are no issues), or
the thing you deliver the PWM to does not need a smooth supply (motors, lamps, heaters, etc all fall in this category).