A couple of these overlap significantly with other ideas that have been recently discussed, so I'll point those out here.
As Kyle noted, this use case is subsumed by opaque parameters, a Swift 5.7 feature that was recently accepted and implemented as SE-0341. This example would be written as:
func doSomething(with value: some Any)
SE-0326, which is under active review right now, composes with SE-0341 to allow one to specify, e.g., the element type of generic collections. Your example doesn't translate precisely, but it's very much in the same space. I do think it makes the case for your suggested syntax a much harder sell, because it's eliminating the angle brackets entirely in a subset of the use cases.
I think generic computed properties would be a good feature on its own, and is orthogonal to the syntax you describe.
There's an active pitch on implicitly opening existentials that's in the same spirit as this.
Another separable and good feature, which we often call "parameterized extensions".
Doug