Rule request: no-implicit-null-types

[JoshuaKGoldberg]

For teams with a large code base, turning on --strictNullChecks can take a while. Having rules that do part of the work would help incrementally enabling it.

If a variable or parameter is assigned null or undefined, its type should reflect that.

Bad:

class Person {
    private name;
    public setName(name: string | undefined) {
        this.name = name; // This should be an error
    }
}

[JoshuaKGoldberg]

This is grander in scale than what a linter can do well. Addressing this would need access to the TypeScript language service.

I've started work on this in TypeStat instead.