I think your example is a good motivation example for Existential subtyping as generic constraint.
For the sake of this discussion, I'm gonna use syntax any P vs P to disambiguate between protocol-as-existential vs protocol-as-contraint, but exact syntax is irrelevant.
Image that there is no self-conformance (any Error): Error. But in the generic signature of the Result we still want to be able to use any Error. Signature of enum Result<Success, Failure> where Failure : Error would not work here. But we can fix this if we introduce another kind of constraint - existential subtyping. I was suggesting syntax where Failure : any Error. This constraint means that Failure can be type that conforms to Error, but also any Error itself, and other existentials like any LocalizedError.
Such constraint would allow Failure to be any type which can be implicitly converted to any Error.
let concrete: Failure = ....
// If this compiles
let existential: any Error = concrete
// then this will compile as well.
let result: Result<Never, Failure> = .failure(concrete)
Would such language mechanism cover your needs?