Well, for quite a few of us, the Gear Swap board fills the 'gear rental' gap. Either we pick up stuff at a discount to try out, or we pay full price with the knowledge, that, while there are no guarantees, we'll be able to re-sell that gear for a slight mark down + shipping costs. You don't always get back as much as you want, but at least you won't completely lose your shirt if you realize a 5'x8' cuben tarp is not for you. Sometimes you can even resell for near full price so people can avoid the 4-8 week wait for brand-n
Most cottage places essentially rent their gear now, for the cost of shipping. I 'rented' 3 backpacks before settling on my GG Gorilla. I returned the other two, one to REI an the other to ULA. It cost me $25 round-trip shipping to try an Ohm, but it was worth it to get the right pack. I couldn't take them out of the trail but I was able to load them up and wear them around the block a few times. I did the same with sleeping bags, buying 3 and returning two after trying them out for sizing at home. I'm sure that happens with shelters all the time, getting set up in backyards and even slept in for a night, just so long as you can return them in 'new' condition.
A place like REI does decent business in gear rental, especially, I think for pursuits like winter camping, where the customer has no idea if they're cut out for it and so doesn't want to lay out $400 for a 0F bag and $150 for a pair of snowshoes, etc.
That said, I'd be interested in the possibility of renting gear for a weekend to try out, but off the top of my head, I'm not sure what my price point would be. For example though, Bearikade sells their Weekender canister for $225 and rent is for $5 for the first 3 days and $2.50 for each following day. Shipping varies based on location, and granted the Bearikade is a rather indestructible product compared to a cuben tarp or backpack, but for my upcoming 6 day trip to Yosemite, I could've rented the Bearikade for $40 shipped ( I live on the East Coast)or less than 20% or the full retail shipped cost. For a weekend, if you lived in CA, it'd be $19, or less than 10%. In my case, So those are the kind of price points you're looking at.
Also, I'd be more interested in renting from an established manufacturer of UL gear, like MLD or SMD. I might be 10% of retail with the option to buy + shipping for something like the MLD Trailstar.