It does cost them some flexibility, in that they can't board as soon as they arrive. But my experience is that sitting outside of a plane is generally far nicer than sitting in first class... at least on domestic flights. For international flights getting on sooner would be more desirable.
I've never flown domestic, but that's the way its been for international flights.
It's also there to keep them out of their toilets. When you have 40 people in coach waiting for 2 toilets and 2 unused ones in first the first you gotta make the firsties feel better for buying a more expensive ticket.
If you boarded last, you'd get no pre-takeoff beverage to sooth your nerves.
At some airports, they board the larger jets through multiple doors - First/Business gets their own, and everybody else crams into the other one. I've also been asked to wait to board while the first class gets situated and has their pre-flight drink. (I've also had that pre-flight drink, and it's pretty nice!).