I'm sure plenty of people on here would object to HTTPS Everywhere being default: "but the user typed the HTTP scheme, the browser should do what the user asked!".
That said, the bigger problem is that too many things that HTTPS Everywhere tries to upgrade to HTTPS are only partial versions of the site; you'd probably need something more conservative to avoid too much breakage.
I moved from HTTPS Everywhere & Privacy Badger to DuckDuckGo Privacy Essentials. It does the job of both of those with one add-on.
In response to HTTPS Everywhere breaking things, it does, and I've done tests comparing it and DDG PE and and found sites that would break using HTTPS Everywhere did not with DDG PE. They may simply be doing more testing.
That said, the bigger problem is that too many things that HTTPS Everywhere tries to upgrade to HTTPS are only partial versions of the site; you'd probably need something more conservative to avoid too much breakage.