String.replace does not accept string | (string, ...any[]) => string replacer

TypeScript Version: 2.7.2

Search Terms: String.replace overload union parameter

Code

type ReplacerFn = () => string;
type Replacer = string | ReplacerFn;

function replaceFoo(str: string, replacer: Replacer) {
    return str.replace(new RegExp("foo"), replacer);
}

Expected behavior:
Compiles successfully.

Perhaps the change is as simple as combining the two overloads into a union, though the implications of that change are possibly unpleasant as far as tooling is concerned.

Actual behavior:
bad.ts(5,43): error TS2345: Argument of type 'Replacer' is not assignable to parameter of type '(substring: string, ...args: any[]) => string'. Type 'string' is not assignable to type '(substring: string, ...args: any[]) => string'.

Playground Link: playground link

Related Issues:
#20432 (Array.from)
#20215 (new Date)
#14107 (underlying issue)

Start by reproducing the TypeScript 2.7.2 error with the provided replaceFoo example and review related issues #20432, #20215, and #14107. Trace the declarations or type-checking behavior behind String.replace overload resolution; done means the example compiles without weakening the behavior of the other overload cases.