This isn't exactly a provider, but an interesting project that you may be able to emulate if you feel like you are up to the task.
One could build a few raspberry pi nodes, attach a small backup battery (for about 2-4 hours without an external power source, in case it looses mains power) build a very basic circuit that sends 12v through the SD card data lines if the case is opened while in operation. This wont work if the backup battery is dead, but hopefully the person who may tamper with it does not know that and discharge it before opening it. The SD should also be encrypted using LUKS though, so once powered off it should be pretty hard to get to any of the data.
These could be placed in public locations, mostly in Libraries, where they use a self built DDNS-like service to update a VPS with their current address and status.
One can then use these to proxy their connections, host micro instances of small projects, tor nodes, or whatever they like really.
The biggest danger of this is really someone finding the physical device and finding a way around the "security" system while keeping the machine running. Also, keep in mind, some sysops keep track of MAC addresses and will kick them off if they see suspicious traffic, or even just after a period of time. In most public ethernets you shouldn't have to worry though.
I am not sure about the legality of this, but some sneaky individuals could do it pretty easily and cheaply. With a bunch of these distributed around the globe it would be pretty secure as well.
If you need any more specific schematics or anything, I think you can PM me here.