Though you could presumably just do the same thing with new instructions, i.e. have an instruction for secure zeroing which zeros the data in any memory or cache where it exists but doesn't cause the zeros to be cached anywhere they weren't already.
The surface area for security vulnerabilities is already impossibly high. Do we really want to add "firmware running on a DIMM exfiltrating key material" to that list?
There are security problems with every architecture. There is no fundamental reason PIM should be less secure than what we do now. This is just fear of the unknown talking.