Any system, however good, can be gamed ... and eventually people will come to scam for crumbs ....
If people run a bike co-op to help lower-income riders, or to provide tools, workspace, and advice for people who can afford to take their rides to bike shops but would rather do the work themselves ... then I have absolutely no problem with those folks taking the best parts for themselves .... not many good parts are likely t show up anyway, but good for the people making the effort to help others, and yes, they have earned their rewards.
Ad for the scabs going to co-ops and taking free or cheap parts to sell .... they will eventually find out about karma.
In the meantime, to make sure that honest folks can get decent parts at the co-op ..... absolutely make whatever rules you need.
If I want to ride a working bike to a coop and pick up a part for a non-working bike .... I can (and would) go to the people in charge and explain the situation. "Hey, I can't ride my bike here with a broken X in order to prove I need an X. Do I need to leave a cash deposit, and come back in a week with the repaired bike with the new X attached, so you guys can see I needed it? Should I ride home and come back with the broken X so you can see I need one? Work with me, here .... I am not about to carry a freaking broken bicycle to a bike shop when I have a working bicycle .... how can we make this work?"
Based on co-op employees with whom I have dealt with, we would work out something.