I would actually enjoy that for certain small projects. Rust without the borrow checker is a very elegant language. The borrow checker is great, of course, but it can be a pain to deal with. So, for small projects it would be nice to be able to disable it.
Instead of disabling the borrow checker what should be possible is to promote borrows to Rc/Arc as needed. I would want to restrict this mode to one where it can only work locally, never publishable to crates.io. It would be particularly useful when running tests, then instead of a compile error you can also get a runtime error with better information about the cases the borrow checker was actually encountering.