What if I don’t heed the warning “hides inherited member. To make the current member override that implementation….”

It will not do anything but the method you have there F() is also not polymorphic. It becomes very easy to make mistake in code if you started to use base class reference hence you are warned. Of course it can be what you want, hence the new keyword just make it more explicit

E.g.

B b1 = new B();
b1.F(); // will call B.F()

A b2 = new B();
b2.F(); // will call A.F()

Now, if you add class C with new, it will behave the same as B. If you add class D with override, then F becomes polymorphic:

class C : A
{
    public new void F() { }
}

class D : A
{
    public override void F() { }
}

// Later

C c1 = new C();
c1.F(); // will call C.F()

A c2 = new C();
c2.F(); // will call A.F()

D d1 = new D();
d1.F(); // will call D.F()

A d2 = new D();
d2.F(); // will call D.F()

See this fiddle.