Uhm, isn't that how it works today ? Do you care about how many metric shitloads of storage your cookies take up on client's disks ? Shouldn't you ?

Putting the cost of storage where the decision to store is made is sound economic practics.

You can still have the cookie concept, and have the session id be a random number each time someone sends a tab to the site. The cookie can hold those preferences, and the session id can be used for session stuff. As a bonus, you can then only load the cookie on the first page load, and keep the values in cache associated with the browser random session number, saving in data transfer issues, and losing nothing. And for those that don't need cookies, they get a big win in terms of privacy.