The closest thing I've seen to some form of "sharing" of brewing equipment is when a club has something like a sophisticated and expensive large batch Herms unit, that a club may purchase and allow members to either "borrow" or rent it. Something like this.
And I've heard at times that can be a bone of contention, if one of their members doesn't take care of it, or fails to clean it properly after they use it.
But like monster said the rental of brewing gear isn't really something you hear much about....Especially rental geared towards beginning brewers....Sanitation/equipment usage, being to me the biggest drawback....I sure as heck wouldn't rent any "Post boil" gear like fermenters, and autosiphons, or bottling gear (unless it was a commercial grade bottling line that was in a location and I brought my fermenter to use, and it was constantly cleaned, maintained and sanitized properly.) I wouldn't want to risk using something that the previous user may have scratched or infected.
Except maybe a bench capper (but lots of LHBS rent those out to folks anyway, so that's nothing new.)
So that leaves pre-boil gear, which means a mash, tun brew kettle, burner and wort chiller (if you're not going high end like above) can you really make money soley renting those three pieces of kit? Maybe? But I don't think that should be the sole basis of your business...I would open a homebrew shop that makes those pieces available for rental....For a few buck. Either for the person to take home, or brew onsite...
But if it's onsite, then you'd do better making it a Brew on Premise.
What a lot of people who do BOP's DON'T do is do all grain (except I hear in Japan) most BOPs stick to the much simpler extract brewing. But I think a BOP SHOULD do all grain, and have high end, larger batch system.
If my homebrew shop was a BOP and had computer controlled 15 gallon systems to be used onsite for a reasonable rental I might even jump once in awhile. Especially with a canning/bottling line that is reasonably priced? Especially a can line? If that were the case, there's a couple of beers that I might consider brewing a huge batch of each annually and keep around canned (Maybe brew a 15-20 gallon batch of my house IPA, and Vienna Lager or Cream Ale, keg 5 gallons of each and can up the rest for the rest of the year) and then brew smaller batches of everything else I would normally brew on my own gear.
That way I'd never have a hole in my pipeline AND some of my favorite beers, those that I may actually brew a couple times a year anyway already on hand. I would do something like that if possible over the week I'm off between Christmas and New year, brew on premise a couple of my house beers and knock them off in one brew session. Then concentrate on everything else the rest of the year.
But if you're just planning to rent gear, I can't see that working, unless you went BOP.