I have the same exact issue. Do you have Filevault enabled? I don't see the issue on a Big Sur machine (i'm on 11.4 now) with Filevault disabled, but on 3 others I have the issue. The latest Big Sur machine I built was working perfectly until I enabled Filevault, then the system_profiler timeout error started happening. Happens when you go to About This mac->System Report->Hardware as well.
I'd really love a solution for this!