Certainly such systems can pretty readily exist. You merely need atomic reads/writes in order to implement locks.

You can't create userspace locks which is a bummer, but the OS has the capability of enforcing locks. That's basically how early locking worked.

The main thing needed to make a correct lock is interrupt protection. Something every OS has.

To go fast, you need atomic operations. It especially becomes important if you are dealing with multiple cores. However, for a single core system atomics aren't needed for the OS to create locks.

> You merely need atomic reads/writes in order to implement locks.

Nit: while it's possible to implement one with just atomic reads and writes, it's generally not trivial/efficient/ergonomic to do so without an atomic composite read-write operation, like a compare-and-swap.

I wrote "multithreaded" but I really meant "multicore". If two cores are contending for a lock I don't see how irq protection help. As long as there is only one core, I agree.