Obviously there's a lot of little details you'd have to work out. Like how to make such a trusted compiler in the first place, and how to sandbox unsafe code and legacy applications that were compiled by an untrusted compiler.
If this seems like it's far-fetched or too much work, consider what lengths high-performance hardware devices like HPC network interfaces go to avoid system calls at all costs, to the point where applications talk to the hardware directly. Is that really a sustainable practice long term? And how can anyone audit the security of such hardware devices?