Rust traits are not subtyping, Rust's type system is principal (although with subtyping you could achieve the same thing as described by the OP, e.g. in C++, C#, etc, which only have subtyping but no existentials exposed as a syntactic feature).

The only reason trait objects aren't subtyping is that impl trait is not a first class type in Rust. They behave like subtyping in this context.