Infinite precision intermediate arithmetic: how much would break?
The research term for this, by the way, is "AIR model" ("as-if infinitely ranged"). As mentioned, it's much easier to implement for integers than floats, and it would be a good idea to treat them as separate problems. (I also agree that retrofitting it onto Rust today is probably a non-starter—even the behavior of implicitly panicking on overflow is probably depended on by somebody.)
I do think allowing mixed-width mixed-signedness comparisons is more viable; Swift managed to pull that one off. Even that can cause confusion sometimes though, for people used to C semantics.
(Alas, "this is what Lisp and Python" do is brushing over the hard part. Those languages will implicitly allocate when numbers get big, but they won't panic, saturate, or wrap the result; it just stays as is. Every number in those languages is effectively a bigint, some of them just have optimized representations.)
Discussion in the ATmosphere