Wouldn't an ideal diode active rectifier be the thing to use nowadays rather than inefficient and heat-spewing 2-diode drop rectifiers? Like an LT4320. Assuming you didn't want a switching power supply.
Depends upon the application and design trades (including cost). Please take these as off-the-cuff thoughts about something not in my main area of expertise.
Diodes are cheap, reliable (mostly), simple, and the voltage drop is not a concern in many applications. Adding a diode controller like the LT4320 and using MOSFETs (or whatever active device you choose) plus supporting components (typically clamps across the controller to prevent overvoltage surges, perhaps diodes across FETs if they aren't built-in like most power FETs these days, etc.) is a more costly solution. Often significantly more costly just for components, plus the additional board area. Design is more involved since you have to match the controller's drive capability to the active devices for things like gate slewing current, and may need to add additional snubbers or other components to limit RFI from switching the gates. Gains include lower IR drop and thus less wasted energy, cooler operation of the rectifiers (less heat) and perhaps less in the way of thermal structures around the rectifiers, and more control of things like in-rush current. Over voltage/current monitoring and protection could be built into the controller (though in my
very limited experience is usually a second chip).
Are there fully integrated solutions for lower-power applications? I do not know, but seems like a market exists, and then you'd have a single-chip solution. Chances are those applications are using integrated SMPS instead, however.
In any event, as far as the original topic, rectifier choice is irrelevant in showing how a conventional full-wave rectified power supply works. One of the things really neat about ASR is the high technical level of the contributors. These basic overviews of mine are mainly for lay folk, e.g. audiophiles interested in learning a bit about the stuff "behind the curtain". It'd be great to shift the detailed discussions into new threads where we could dig (much) deeper.
Interesting thought - Don