Soon enough, computers will have a system where all you buy is the monitor with an ethernet jack. The computer itself is somewhere else in the world with incredible hardware, but you get to control it locally. Can you imagine the possibilities with this?
You've basically described a
thin client.
Not really the future, because physical computers will never become truly obsolete. Especially considering a remote connection would NEVER be done for the government, makes hacking way easier.
I'm not sure I understand your post. These sorts of connections are done all the time by the government and private companies and have been done for decades. Traffic encryption is easily taken care of using some sort of VPN client and a Verisign, RSA, or similar security token on a keychain in addition to a standard password login. It's true that most places have a policy against using public computers (like a library) to access content, but there is nothing stopping me from sticking a bunch of rack mountable computers in a server rack and just issuing a monitor, keyboard, and a booksized computer that basically holds a network interface and a graphics card to my employees. There can be maintenance, power consumption, and efficiency advantages to this setup, and it's no less secure than a normal office setup.