I can easily create a Windows or Linux desktop machine in the cloud at Digital Ocean or Vultr.com for very little money and access it with rdesktop and/or a VPN. Amazon has a slightly more "enterprise" desktop-in-cloud offering that's basically the same idea.
A lot of the underlying technology for paperspace certainly exists today and its best to think of what we are doing as providing a layer on top of it all (and polishing the pieces that didn't work so great before):
To give an analogy, cloud storage was definitely around long before dropbox and google drive. It was simple, I uploaded a file to FTP, you opened your FTP client, and we could share files. The reality was that less tech-savvy people might never get past the install step.
What dropbox/google drive/box did was take an existing (and increasingly commodity) offering and wrapped it in a layer that made it accessible to a whole new class of users.
Digital Ocean is amazing and we are shooting for the same simplicity for full desktop computers.