Apple has not failed with the mini because it never tried for this sort of thing in the first place - it is a happy accident. And one that I believe they noticed and allowed to go on organically with the bare minimum of effort on their part.
The reason collocating minis is intriguing is this: This consumer grade hardware has gotten so reliable and powerful that it makes for a very good server - being a consumer SKU means it has a production run orders of magnitude greater than a Dell server for example.
Thus a Mini is disposable. It is almost like a Raspberry Pi.
A proper server will obviously be more bang for the buck in terms of raw hardware specs, but the TCO of a Mini is favorable because you can resell it and it has a good, none-enterprise-y warranty.
A fully loaded Mini amortized comes out to something like $50/month. It also blows EC2, 'etc, completely out of the water.
In the rather rare case of it failing it is simply swapped out by the facility with exactly equivalent hardware in short order while yours gets handed off to Apple Care, at which point you can simply ebay it for 70%+ of its original price and get a brand new one switched back, all in a matter of a day or two. If you need to "spin up" more, there are always more laying around that can be provided by the facility immediately. Dedicated hardware that is so flexible and convenient is a powerful thing. Depending on your use case you could get away with running on just a couple of minis and save quite a lot of money.
If you buy them in threes for redundancy Apple offers nice discounts and financing. You want to compare how much performance you get out of three minis for $200/mo (total) to what that would cost you on Heroku?
Oh and I'm pretty sure you can boot linux from an SD card or some such.