I can see it both ways, this would incentivise doing proper run-up checks and would be pretty cool on the whole. The only doubt about a system is when you start running into inspections designed to catch certain faults; like pre-flight, daily, 40, 120, 360 and 720 hour inspections (Hours are airframe dependent). At those intervals, the aircraft should in theory be reset in terms of any faults that may arise and to be good to go. You can't really crawl around the aircraft to see if a filter button popped, find leaks in the hydraulics or general wear and tear either, so that's no fun.
Besides, after you land at the airfield and repair, everything that's broken gets fixed and you have essentially a brand new aircraft.