Do they though? Do public universities really have competition? Maryland has College Park and not much else. All the other public schools are much much smaller, and generally lower quality.
This isn't the 1850s, UMD essentially competes with at least the other east coast public schools. So you have Penn State and UVA, as well as UD, Va Tech, GA Tech, UNC, etc.
Add to that the negligible degree to which attending "the best school" effects your outcomes (spoiler: virtually not at all. Being in the top 25% at your school far outweighs how good your school is) and you'll realize that they compete heavily. This totally leaves out all the private schools with which they compete in the DC area.
Except not really because the cost for going to an out of state public school is much larger for a student so any given school has a large leg up on cost in competing for students in their state.
Except not really because most State schools on the East coast will give you in-state tuition after you live in said State for one year. Take a year off after highschool, make some money, then get in-state at whichever school you chose.
Source: many of my friends graduated college a year behind me after doing exactly what I'm suggesting.
Add to that the negligible degree to which attending "the best school" effects your outcomes (spoiler: virtually not at all. Being in the top 25% at your school far outweighs how good your school is) and you'll realize that they compete heavily. This totally leaves out all the private schools with which they compete in the DC area.