Https is a protocol. That means both sides have to agree upon it. Even just this would make things a bit weird - what would the browser do, try and connect over https, then if that fails, fall back to http, and cache that decision for some amount of time? If something on your site changes, how do you communicate that to the browser to get it to refresh its cache? There's a series of practicalities here that would need to be worked out to make this actually happen in the real world, and they haven't been yet.
Beyond that, not every site that accepts an https connection actually works over https. As a simple example, the New York Times website listens on port 443, but if you change the url for an article to be https, it will just redirect you back. If the browser did its own https redirection automatically, this could very easily put you in an infinite redirect loop; at the very least, you would be waiting through two http requests for every page instead of just one.
There's usually more work to be done in making a website https-available than just setting up an https terminator (although even that can be a bit of work, as you need to load test it to ensure it can handle your entire traffic - I once broke a previously-nicely scalable website by skipping this step). One of the biggest issues is making sure that all the content you embed in a page is also requested over https, or else you'll get mixed content warnings, and the user will just see a broken page. This can be particularly annoying to do if you have user-generated content, because now you've got to do some database munging to fix things they've been adding, and be very careful to make sure you don't screw something up while doing that. And now you've got to use https on your CDN, and some still don't support that easily, or maybe you have to upgrade your plan to be able to use a custom certificate (since you had a CNAME from your domain to their servers). And now that breaks some scripts you have, because they're written in python 2.6, and that doesn't have SNI support.
The list goes on. The point is, there's actually a non-insignificant amount of work for many websites to transition fully to https, and if a browser tries to force them all the way all at once, there will almost certainly be broken things. And that sucks for users.