The pilot has no
idea what "Potomac" is (from a routing standpoint)
The controller does. Ask him.

Supposed I asked. What would the answer be? (I'm more interested in
how long it would take for the controller to communicate the relevant
information).

Therefore ATC is in a good position to offer helpful alternatives. They
are refusing to do so.
No they're not.

Yes they are. We're back to Monty Python. The pilot wants to get to
his destination efficiently. The controller knows what's 'open' and
what's not, or is at least in a much better position to ascertain this.

The pilot can ask, ATC can't read minds.

ATC can read flight plans. Doing so would provide a clue as to what the
pilot wants, unless things are so balled up that there really isn't any
good way to get to the destination. In that case, ATC really doesn't
know what the pilot would want. Otherwise, it pretty much goes without
saying that the pilot wants to get to his destination, and that makes it
reasonable for ATC to offer reasonable alternatives.

Let's see if I can learn something, and turn this around.
Oooh, something new!

Actually, I learned something once before.

"N423YL, Potomac is refusing to handle you. What are your intentions?"

How do you respond?

I respond with, "Never mind that center, my route takes me in between
building TCU. N423YL requests clearance to Richmond via direct."

"Unable direct Richmond, that takes you through Potomac. What are your
intentions?"

I made that up; I'm pretty sure that you know where Potomac lies and
picked a good route, but if it were an unfamiliar approach, you might
not reasonably know that direct wherever would take you through the
closed approach. So, pretend with me that you didn't know the area, and
are now faced with my reply.

At some point you are likely to ask for suggested routings, and that's
where I think the controller should have started.

Jose
--
Nothing takes longer than a shortcut.
for Email, make the obvious change in the address.