Thanks. That is a very good question.
I used to volunteer at Hackney Bike Workshop so I think I understand the issues.
Part of the answer is that a repair café is not a free repair service: it’s about helping people to fix their own stuff.
The person bringing the thing to be repaired should be encouraged to help with the repair as much as they can. Obviously in some cases (learning difficulties, disabilities etc.) they won’t be able to help much, but at least they see the repair being done and they don’t just leave the item and come back when it’s fixed. If they try to walk away while their item is being fixed, we stop working on it.
This will put off people who just want a free fix.
An important point is that this is a free volunteer service: we’re not obliged to fix everything that comes in and we can refuse to help people for whatever reason we want, including, for example, people taking the p*ss and trying to use it as a free repair service.
Another point is that the repair café is time-limited so if someone wants a complex repair (e.g. a complete drivetrain replacement: crankset, bottom bracket, chain and cassette) it just ain’t gonna happen in the time available even if they bring the parts, so in that case we can do local bike shops a favour by directing that person to a local business and giving them a bit more trade 
.
Alternatively we/they can do part of the repair and tell them to come back next time, which, again, will dissuade the scroungers who just want a free repair.
We should do the research and make sure we’ve got a list of any/all the local repair businesses (not just bikes) to display so we can encourage people to use them.
As @Dorine said, it’s also about increasing accessibility: not everyone can afford to pay for repairs: for some people a bike is their only mode of transport other than their legs.