I find reflexive impls to be pretty frustrating in Rust. They get in the way of endless conveniences for traits like From and Borrow, but at the same time they're great for automating boilerplate and enforcing consistent behavior. I even use blanket impls in my own projects, although I often end up replacing them with manual impls once I realize I want a special case for arrays, tuples, options, etc.
This would most likely be resolved if specialization ever stabilizes, but as an alternative: what if there was a marker trait that represented "simple" (non-complex) types?
Most primitive types (bool, i32, Duration, etc.) would implement this trait, while generic structures (Option<T>, [T; N], (T,U,..), etc.) would not. In general, it could be implemented for non-generic types automatically unless they explicitly opt-out with a negative impl, while generic types could explicitly opt-in with a manual impl.
Consequently, reflexive impls could be changed to impl<T> Trait<T> for T where T: Simple, and non-simple types would be able to provide specialized impls (e.g. impl<T, U> From<Option<U>> for Option<T> where T: From<U>).
Backwards compatible? Probably not, unless everything implements Simple and has to explicitly opt-out by default (even generic structures). In that case I think it would be backwards compatible, so long as the standard library opts out of Simple and provides impls where relevant.