That might not be the worst idea - having just 8 non-league clubs (presumably the 4 semi-finalists in Junior/Intermediate Cups or even keep the Prelim round for all 16 Quarter-finalists).
The problem really, isn't so much the standard, but the timing for them. When we played Bluebell last year they probably only had a handful of training sessions under their belt. I think Oliver Bond were similar when they played Derry. So there is definitely the potential of reaching the last 8 without even facing a league side, your suggestion reduces that chance and does solve for fixture congestion for the European clubs (for one game anyway!).