Can too big hosted mining service be mitigated by allowing customers to choose mining pool? Let's say a company is hosting mining hardware, either hosting customers' hardware or renting out the hashes produced by hardware owned by the company, or both. So the company is physically controlling the hardware.

What if this hashpower reaches a percentage of global hashpower that makes double-spends possible.

Can this be mitigated by the company allowing customers to select which mining pool they want their hardware/hashpower pointed at? For example through the company's web interface.
I think it primarily just gives you a false sense of security.

Let's say company XYZ is a hosted mining company like you describe. They grow so that they have 51% of the network's hash power. This may not be apparent on graphs like this one since it's spread among other (reasonably-sized) pools. However, since they are ultimately in control of the hardware, they can "go rogue" and make all of the hardware mine on their own pool. They now are able to execute double-spends, since they have 51% of the power. Note that this will not be a quiet thing: People will know that it has occurred.

A major reason why this probably wouldn't actually happen is that the company would be killing their golden goose. They could keep making money as a mining service, profiting from Bitcoin's success; instead they succeed in a few double-spends and then faith in Bitcoin is destroyed, and the value plummets. Or, since they no longer have cash inflow from new miners, they can't keep up with the rest of the network's improvements and they fall below 50% of the power. Either way, they're pretty much shot.

If we had a way to provably protect the hardware (via some private/public key system) so that the renters are really the ones that control what pool it points to (and the communication between the pool and the hardware was similarly tamper-proof), we could prevent this sort of attack completely. This would make the service more like a "customer buys some hardware, and we provide the space, power, and cooling in exchange for a fee" service than typical mining contracts.