Simplest Linear PSU?

Transformer, Bridge Rectifier and filter caps.....

yes, that's the simplest but likely not the best.  For constant current draw stuff, multiple filter stages can be very very good, and sound remarkably right. but for anything requiring specific DC levels (like any ICs) or current surges, it has major issues and regulation is required. regulation brings its own issues and noise sources.

This is why i somewhat push back on the most  basic tenets espoused in this thread.

@itsjustme +1 I use Uptone JS2, choke based lps on some of most important digital components. This will explain issues with T,BR&F  and advantages of choke based,https://audiobacon.net/2021/08/06/the-worlds-best-audiophile-linear-power-supplies/3/

I am a fan of small chokes to eliminate the HF noise generated by most series regulators. 

I should add that the link above describes what appear to be very well thought out supplies, at a not-insane price considering what's inside them.  I pay little attention to the stand alone LPS market since i design LPSes for use within products. And when i need my own personal outboard LPS i just build it ( i have genero PCBs that i fab and can adapt to most uses).

Regulation done right reduces noise on the supply, rather than adding noise.