This is exactly why browsers warn about such redirects. That said, this reminds me of a similar discussion on mail servers. There, STARTTLS sees much more use.
The main problem is preventing downgrade attacks. With mail it is easy to just remember the setting for every server. Not so with websites.
I've seen quite a bit of criticism of it for mail servers [1] because an attacker can simply block the 'STARTTLS' message and (many) clients will silently accept that.
I'm not sure you can assume that the same URL with https will be the same content as at http. It could be an entirely different site that you may not have wanted.
That isn't really viable yet. Browser vendors could decide that they will introduce this functionality in a few years though.
IMHO, the feature would need to be implemented as some have suggested, by enabling any website to transmit securely or insecurely, but for the web browser to request a secure TLS connection first (trying HTTP and HTTPS to reduce incompatibilities) and if a website appeared to have issues, then try insecure connections. If an insecure page were to be served, the browser should indicate this with a broken padlock.
Furthermore, I believe that browsers should warn when any data is input, e.g. clicking items that cause JS calls or text is typed - this strict implementation is important. Single page JS applications have made it possible to send any input data via JSON, we cannot only warn the user on a form submission, since it would be very possible to capture details via AJAX. E.g. If I were impersonating an e-commerce solution, I could hope the user would not notice the padlock and use AJAX to send the data preventing any form submission warnings. This would be annoying for users when they were using such websites regularly, but this would be a good thing - pressuring websites that handle user inputs to act responsibly and use encryption via TLS.
A good solution for HTTP sites is to load the https version after first loading over http. If they have similar content, show a bar at the top of the browser with a message along the lines of "A secure connection is possible, click here to go to use the secure version of this page".
Then it would be good to remember this setting and always pull the HTTPS.
Why not expect it to be secure? Connect to https before http.