That's being tried: https://www.crowdsupply.com/sutajio-kosagi/precursor

"The principle of evidence-based trust was at work in our decision to implement Precursor’s brain as an SoC on an FPGA, which means you can compile your CPU from design source and verify for yourself that Precursor contains no hidden instructions or other backdoors. Accomplishing the equivalent level of inspection on a piece of hardwired silicon would be…a rather expensive proposition. Precursor’s mainboard was designed for easy inspection as well, and even its LCD and keyboard were chosen specifically because they facilitate verification of proper construction with minimal equipment."

See also: https://betrusted.io

This is somewhere in the 10x-100x more expensive and consumes much more power, for lower effective clock speeds. It's not a production solution.

In addition to what the other comments have already highlighted, there's also the fact that you'd be back to using extremely opaque, even less "open source" hardware than regular CPUs/MCUs. Almost every FPGA that could even conceivably be used to run general purpose software is locked behind super proprietary stacks