It has nothing to do with Spectre. Spectre exploits Intel's (and tbf others') mistake of changing the processor's global state when speculatively executing code. Intel could fix it either by always checking permissions before spec-ex, or by transactionally rolling back all global state changes (e.g. cache lines) when permission failures are detected.

Edit: I misunderstood your question. Yes, Spectre cannot be fixed with software. But if Spectre were fixed in hardware (as it must be in new designs), software process isolation could still work barring new undiscovered hardware vulnerabilities.

Isn't eBPF basically the same idea?