If anything Spectre has shown us that the only real mitigation is to go back to multiprocessing with IPC, with the extra hardware resources it entails, as the exploit exists regardless of the language for in-process memory.
If you were do to do per process mitigation it would need to prevent certain process execution flows from happening, because the vulnerability is a problem with the CPU pulling memory from the way speculative execution works. This actually impacts things that are typically protected and is much more impactful than people think... for example, because the bug allows reading from nearly any memory address space, you could also pull in things like crypto keys from the OS or passwords from memory.
For example, a speculative execution vulnerability might exist when there is a string of data in memory that has a memcp pattern, with memory addresses that are valid. To speed up the execution of programs, the processor might proactively read the memory from that memcp pattern because it is sending a command to the memory controller already.
Many of the mitigation techniques are to flush the caches/buffers and be careful about memory reads, which are the precise things that actually take the performance hits. And one of the problems is since they are access patterns, the vulnerabilities can be the html renderer compiled with an application, an SVG rendering library or a mail client.
For example, lets say there are mitigations built into the JS library... if you build a specifically crafted SVG, you could create similar access patterns to get around it. Its a huge cat and mouse game if there aren't OS protections and it only takes a single app to lose your secrets stored in memory.
Now it is not possible for every kind of mitigations, because e.g. patching the kernel between mitigated processes and unmitigated ones would be more costly than just always running the mitigations.
edit: thinking more about it: you could have crazy ideas like two versions of the whole kernel space always loaded :D not sure about the cache impact in this case though.
Per-process Spectre mitigations could be helpful there, but I don't understand the technical details to know whether that would be possible to implement. It would be nice to disable mitigations on a video editor and for gaming.