I'm not talking about standardization but about a different kind of type system, where the intersection types of callees interact in interesting ways with the type of the caller[1] (taking into account ordering). From what I understand this kind of thing is being research but we don't have anything close to being practical just yet.

Isn't chriswarbo's example that? Since your Ops are generic they can be other effect types. The interleaving is the tricky part, but e.g. Haskell's extensible-effects is practical enough that it's used in real programs.