I think if you try to responsibly design this feature in browser UI, you'll end up with the same problem.
User requests an HTTPS resource, which means the connection must be secure. The UA is unable to establish a secure connection, just as if a MITM attack was underway.
So, now, the user has just entered https://facebook.com. Currently, when this secure connection fails, the browser warns the user in no uncertain terms.
Your suggestion would be to what, exactly? Put a small, unobtrusive dot somewhere in the UI indicating "yeah, I know you asked for HTTPS, and I ignored that, but I didn't wanna really bother you"?
If you're responsible for user's safety, which may depend on the UA treating HTTPS as it should, then you've just betrayed your user.
And at any rate, by not aborting while verifying the certificate, you're already leaking potentially personal information: The URL, cookies, etc. So if you treat the user's data with respect, you don't go sending that insecurely after the user requested HTTPS.
And if you can't transmit the request, because you need to warn the user... you end up with a UI like browsers have.