Sorry I didn't see this earlier. Looks like sift is broken by #17912. I'll go check it out.

I think the sift errors are legitimate errors in their .d.ts. at least that's the conclusion we came to in Friday.

Maybe. Here is a clearer repro:

function f<T extends any, P extends keyof T>(tp: T[P], aa: any[]) {
    aa = tp
}

The question is whether the constraint of T[P] is any when T extends any. I would say yes. Right now the answer is no.

After some investigation with @mhegazy, the picture is much muddier.

1. There is some precedent for not making T extends any equivalent to any. Partial<any> is not any but { [s: string]: any }.
2. sift.js did not intend to constrain T extends any. They found it as a convenient workaround (that partially destroys their intended semantics). I don't think anybody says T extends any intentionally, in fact.
3. sift.js actually wants everybody's favourite infinite type that escaped from Lisp: type Tree<T> = T | Array<Tree<T>> (where T is not Array). This isn't really possible in Typescript until conditional types happen, and I'm not sure it's possible then.
4. @weswigham noticed that T extends any === any might interact badly with conditional types as currently implemented, so it's safer to leave this change until after those are done.

It's an easy change to make, but until there's more demand, I don't think this change is worthwhile.