Earlier quoted context omitted.
Can't edit my original post anymore: Firefox and Chrome do seem to isolate even same-browsing-context-group and bridge the required APIs via IPC, so hopefully Safari will catch up at some point. Basically, there are three scenarios: - Completely unrelated tabs (e.g. those you open manually, those opened via command-click, tabs opened via ' " or 'rel="noopener"' references etc.) – these are relatively easily isolated…
I worked on a browser team when Spectre/Meltdown came out, and I can tell you that a big reason why Firefox and Chrome do such severe process isolation is exactly because these speculative attacks are almost impossible to entirely prevent. There were a number of other mitigations including hardening code emitted from C++ compilers and JS JITs, as well as attempts to limit high precision timers, but the browser vendor…
Can you make a "Secure" CPU? In theory yes, but it won't be fast or as power efficient as it could in theory be. Because the things that allow those things are all possible side channels. This is why in theory the TPM in your machine is for those sorts of things (allegedly, they have their own side channels).
The harder question is "what is enough?" e.g. at what level does it not matter that much anymore? The answer based on the post above this is based on quite a lot of risk analysis and design considerations. These design decisions were the best balance of security and speed given the available information at the time.
Sure, can you build that theoretically perfect secure CPU? Yes. But, if you can't do anything that actually needs security on it because it's so slow; do you care?