Does there exist any platform which has multithreading but not atomics? Such a platform would be quite impractical as you can't really implement locks or any other threading primitive without atomics.
Yes. Also, almost every platform I know that supports multi threading and atomics doesn’t support atomics between /all/ possible masters. Consider a microcontroller with, say, two Arm cores (multithreaded, atomic-supporting) and a DMA engine.
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.
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.