Tis an interesting idea. Shipping a rig with already-installed, extremely heavy video cards is a bad idea though, which means you would have to have people ship their rigs without the video cards installed, and you'd have to deal with installing them yourself.
You could charge a base amount for a tower, then additional based on electric usage. With high usage throughout the facility, you should be able to negotiate with the local electric company down to rates like $0.03/kwh. That would help make up the difference for what it costs to rent the facility. You'd have to have a way to track total electric usage for each rig each month, which could end up being expensive. Or you could do it the ghetto way, and just have each rig run through its own kill-a-watt, writing down the data each month and resetting it.
You could offer "rig reset" requests, so that if someone needs a hard reset done on their rig, they submit a request through some web panel, and then next time you are at the data center, you can reset the rig manually. Or better yet, rig up some sort of PLC that is controllable from the web interface that allows them to cut power to the machine if they like. Just remind them to set their BIOS to power-on after power loss prior to shipping the machine to you.
One potential problem is having each rig on the same network. I suppose you could say that each person is responsible for their own rig's security, but that could fall apart if someone hacks into another person's server from their own server and hosts something illegal on it.
I'm not sure there's enough margin in in mining anymore to make something like this profitable, but let's take a look.
Take a typical mining rig: A Sempron with 3 5850's. It probably draws about 500w under full load mining. Ok, so charge a base fee of $25 and $0.15/kwh. Assume that your actual electric costs are $0.035/kwh, and that you use twice the actual electric draw per rig (to counter the heat produced by the rig, you must have A/C to cool it).
This rig would cost you $25.20/month in electricity. It would bring in $79/month in revenue (paid by the miner). It would make the miner 0.61 BTC/day, conservatively (assuming 333MH/s from each of them), or about 18.33/month. At today's prices, that's $256.66.
So the miner makes $177.66 profit, you make $53.80 profit.
How many such rigs would you need to employ to cover the rent of a facility? Probably not a whole lot, as small rental offices can be had in my area for a few hundred a month. 8 rigs might be enough to cover the rent for a small office area, and a 9th to cover the internet expense. But, you'll likely have to upgrade the A/C and electrical prior to starting the project as well, which means higher capital costs that must be eventually recovered.
Interesting thoughts though. I think there's definitely a market for it, but it might be difficult to find someone willing to take on the risk of spending a bunch of money on remodeling a rental whose sole revenue is reliant upon bitcoin mining continuing to be a profitable operation.