And someone has in fact managed to get MMU-less Linux running on the newer Pico 2:

https://github.com/Mr-Bossman/pi-pico2-linux

That's with an 8MB external PSRAM though, fitting modern Linux in the internal SRAM is probably a step too far.

I used to work with a Cortex-M3 port of uCLinux, but it was kind of a pain to manage. The biggest problem being every executable had to be statically linked to all of its dependencies.