You said

Remember, Qa2b3 means that there are three queens, potentially at a2, a4, and b4

Now in your reply you are showing a queen at a2, a3, and c2, and in this case there's no argument that Qa2b3 is unambiguous and necessary.

Please understand, I wasn't disputing the occasional need to use both rank and file, just querying how you could deduce the existence of three queens from Qa2b3

So forgive me if I misunderstood you, but perhaps you can see how my confusion arose.