Hi Dominic,
I would agree that follow up is likely to be more productive but you underestimate the determination of the amateur. It has already been done
https://arxiv.org/abs/1804.05551
The issue is not so much the precision of amateur photometry or lack of untouched sky to explore but the numbers game. You have to spend an awful lot of time looking at an awful lot of stars to find one transiting exoplanet candidate and even then you need luck. You would need a survey on the scale of the one run by Stan Waterman for example who found a fascinating gamut of variabilty in his “Kepler before Kepler” survey but no planets as far as I recall
http://www.stanwaterman.co.uk/variablestars/
Cheers
Robin