I dunno. In my universe borrowing bikes has pretty much always been a case of being somewhere where person B is and your bike isn't and using theirs for some one-off purpose. The relationship between you and person B is pre-existing.
"Can someone lend me a bike?" requests to strangers require a medium that reaches a reasonable number of bike owners and a context where they have at least some idea of how to track you down if things go wrong. I suppose in ye olde days this might have happened via, say, a noticeboard in a student hall. But by the time I was a student, that sort of thing was mostly usenet-based, so doesn't count. Similarly, the YACF community of cyclists is also IT-based so doesn't count. Real-life cycling clubs probably do a bit of this, I suppose, but they're of limited interest to people without bikes.
A tool for matching bike renters with owners of suitable bikes seems like a good enough idea. Registration, charging and taking a cut seems fair - you can't build and maintain something like that without cost. It's useful in the same way that eBay is useful, and just as eBay doesn't stop you selling your spare widget to someone you know for cash, it won't stop people lending each other bikes independently.
Putting strangers with mutual interests in contact with each other is surely the greatest thing about the Internet. Creating opportunities for people with a Mk 1 good idea to build a business around it is another. What's not to like?
ETA: Crosspost with Dibdib