Actually, mainstream CPUs do use error detection and correction for internal operations and memory.

https://en.wikipedia.org/wiki/Machine-check_exception

Realise that if you only protected RAM with ECC then you're leaving a lot of data vulnerable in caches and registers, so those need parity bits too (as well as lots of other error checks on CPU operations). And anyway, CPU errors are common due to bad power supplies and overclockers. And you don't want to add a whole lot of design effort to create a marginally cheaper-to-produce version of the CPU which doesn't do any error checking.

I've seen a lot of MCEs on non-ECC CPUs :(

IANAEE