Perhaps I am missing something here, but given that everyone was advising against renting a car and do drive by visits and to do Uber instead, I am wondering how an Uber driver would avoid the same traffic from the airport as OP would experience?

Are Uber in Washington allowed some special driving lanes of some sort that would shorten the ride, thus reducing the transport fee?

Given that the OP comes in late on Saturday night in December, which some have stated to be lighter traffic and will more than likely have parking options available, this may not sound so bad.

I am not from DC, so I can't make any strong recommendation in anyway, although I did visit and used the metro there.

If I were to go (and this is based on my preference), I would stay by the airport. Rent a car for the $40. Drive by various monuments, etc., as you most likely won't have much time and the weather may be colder for extended walking around. Then have dinner somewhere in DC. Drive back to airport and return rental car early. Have a good night sleep, and wake up early enough for airport shuttle to take you to airport in timely fashion.

Again, this is my personal logic and from someone who has been to DC only once, so it may not sound all that logical.