Meltdown and Spectre cannot be properly fixed. The proper fix requires a different design of processors that does not rely on speculative code execution as a starter for performance gains. Running processes on different physical cores does help to properly mitigate Spectre. But there are only so many cores a CPU has.
New headers for labeling the sensitivity/security requirement of page should be made. Some sites/apps like banking, shopping need very high security.
Websites should have new headers to indicate the user’s agent to take appropriate steps.