Site isolation mitigates variant 1 of Spectre, which allows same-process reads.
It doesn't protect against variant 2 of Spectre, which could allow cross-process reads. While this is believed to be much harder to exploit than the first variant, there are several mitigations in development:
- Reduce the reliability of timing gadgets from JS
- Compiler defenses like LLVM's -mretpoline
- Intel's IBRS microcode update
As you mentioned, site isolation also won't help against Meltdown, which allows disclosure of kernel memory: this requires the kernel page table isolation patches.