Why are hotel rates so expensive in Washington DC?

They are in demand, so they can charge those prices and receive bookings at those rates.  There are a lot of people traveling to DC for work, for vacation, for medical care, etc.  When there is a lot of demand and hotels are busy, rates are higher.

We usually stay just outside DC, somewhere in Arlington and along the Metro line. Rates are considerably lower, but it's still quite convenient to most things we want to see and do.

Here's another vote for staying outside of the city.  We usually stay in Arlington, and have also stayed in Alexandria in the past.  Hotel prices tend to be better, and we've always had good luck with the metro.  When we go in the winter, crowds are much lower, and we have been able to drive in and find parking easily.

www.choicehotels.com sorted from low price to high starts at $51/night. I just did that, I didn't explore how much driving they are away from the Lincoln Memorial or anything.

Basic law of economics, supply and demand.  Same applies to other cities like New York, Boston, San Francisco etc....

Because demand for rooms is high. A lot of people are in Washington for business and government and it's a popular holiday destination. You can find some places in DC that are cheaper or stay outside the city and take the metro in if you use a site like Trivago or Hotels.com.

1. There are a lot of travelers who aren't paying their own expenses, and don't care about the cost, so the hotels can charge as much as they want. (When a company the size of Boeing sends someone to lobby for a contract to see dozens of airplanes to the military for 500 million per airplane, they don't mind paying a few hundred for a hotel.)

2. There are a lot of companies that want office space there, and there aren't skyscrapers (except for the Washington Monument), and a lot of the land is either protected wetland or owned by the government or bad neighborhoods. The competition for (usable) room is pretty intense and drives up the prices.

You can save money by staying somewhere in Maryland or Virginia that is less expensive but is near a Metro stop.

Yes, they are high, but they are typically as high in most US cities (look at the rates in New York).

They are high because rooms are in demand.  Lots of visitors: tourists, business travelers, folks attending conferences, "marchers", lobbyists, international diplomats--you name it.

You can find somewhat better rates in the close-in suburbs, such as Arlington, Virginia.  Just look for locations close to a Metro subway station.  As a bonus, they will typically include free parking and often an indoor pool.