A lot of people might find the idea fun, but actually sitting around in some remote base, just waiting for the next wave of drones to come? Even if you draft those people "for free", they could be working (or raise a family) instead, so the human cost is always there.
In WW2, the US lost ~15000 airmen just in training accidents to crew the ~300k planes it built. I'm sure we could get that rate down substantially with modern simulators and safety investments (=> also not free), but human lives simply got comparatively more expensive (and competent pilots were not that cheap back then either).
The attacker, meanwhile, is certainly gonna lose less men building and controlling the drones, and he can afford at least 10 attack drones for every interceptor you build.
If you did something like this on a larger scale, a big concern would also be that your manned interceptor aircraft simply become targets themselves, so the "low-risk turkey shooting" could quickly degrade.
I do expect (non-suicide?) interceptor drones as countermeasure at some point (specifically against the "cruise missile with props" style of attack drones, less so in the FPV weight class), and those could be conceptually quite similar to old prop fighters.