You don't even need to do that. You should need administrator access to install software initially, but that installation process can set up a system service that handles any subsequent updates automatically. This then runs independent of any current user on the system, and therefore does not depend on their personal privileges, nor does it need to prompt anyone for permissions for every update.

Clearly there is a risk involved with any process that can automatically download code you will subsequently execute. However, with proper access control, at least a compromised application running in user space can't do things like modifying its own executable so the malware has a place to live or, more generally, anything else that the user couldn't do without elevating their privilege level.

This certainly doesn't get us to an ideal security model. As I noted elsewhere in this discussion, a user on most systems today can probably still do things like e-mailing all the sensitive work documents they can access to a hostile party with just their normal privileges. However, it does at least prevent one common kind of attack.