I'd like to focus specifically on the question: "Does this proposal fit well with the feel and direction of Swift?"
Recognizing that there is value in getting this protocol incorporated in time for the Swift 5.1 ABI, just as there was value in having Result in time for the Swift 5.0 ABI, I hope that there will be a plan of record in short order as to how better to integrate into the rest of the standard library.
Our documentation for ObjectIdentifier reads as follows:
In Swift, only class instances and metatypes have unique identities. There is no notion of identity for structs, enums, functions, or tuples.
This obviously will change, and changing the documentation is straightforward, but it is an indication that this protocol does revise existing assumptions built into the design of the standard library.
If what's proposed here had originated from within the standard library itself instead of being an existing protocol sunk down from SwiftUI, I imagine that the more consistent naming would have been CustomIdentifiable (in the same vein as CustomStringConvertible). We would then say that all class instances and metatypes have unique identities by default, and structs/enums/functions/tuples have no unique identities by default, but any type that can conform to a protocol can be given a custom notion of identity by conforming to CustomIdentifiable.
Along the same train of thought, it would then make sense for ObjectIdentifier to have an initializer init<T: [Custom]Identifiable>(_: T), and it would be reasonable to have a discussion as to whether ===<T: [Custom]Identifiable>(lhs: T, rhs: T) should exist. (The issue is that such an overload, if we're to go with the notion that the protocol allows for a custom notion of identity, should be preferred over the non-customized version).
None of this needs to happen immediately, and--again--having the protocol in time for Swift 5.1 has value. However, it would be unfortunate if such additions continue to be reviewed on an expedited basis without follow-up to work on the "fitting well" aspect of things. The analogous follow-on discussion for Result, for example, has not yet taken place despite statements of intention to do so.