It does not necessarily solve the problem. The provider could steal the keys in memory when the disc is accessed. Anyway, hosting stuff at home does not fully solve the issue: you still have to trust your machine's firmware / hardware. So… HTTPS should never be used?
The only guarantee HTTPS gives is that the communication between the client and the server is encrypted, not that the server is not compromised. HTTPS does not worsen the situation. Nobody should use HTTPS for authentication, that's not what it is for (edit: well, except the bit about domain ownership, agreed)
Compare that to pure optimistic encryption which has very different properties than https.
[P.s. If anyone says OV and EV certs... those haven't been very effective so im ignoring them]
The argument that if you create a key and put it on a VPS or shared service is effectively giving it to the service provider is true. But what does it matter. If you don't have an element of trust with your provider than where you hosting with them? And if you're that worried about it why not do full disc encryption on top of it all?