I'm not sure why they allow helicopters to fly against the other traffic at that airport. You don't see passenger planes flying past each other like that. This practice was obviously a contributor to the recent collision. I'd expect a change to that in the near future.
Same reason taxiways cross runways at most airports. You've got vehicles that need to be on the other side of the approach/departure path, and the only way for that to happen is if the paths cross.
The airspace in the area is complex, so it's a challenge to provide useful helicopter routes while reducing potential conflict.
The airports I fly at (student rotary pilot) have all had the same traffic for rotary/fixed wing, but the FAA talks about [flying _opposite_ planes at a different altitude](https://www.faa.gov/air_traffic/publications/atpubs/aim_html...) as a potential practice.
My understanding of why (and also why we're cleared _direct_ a lot of times) is that we move a lot slower than planes, and that ends up being dangerous in its own right in a pattern shared with planes!
But think of all of the dignitaries who would have to be driven around DC in traffic as opposed to being flown on helicopters to where they need to go!
These people see themselves as aristocrats. You don't expect them to travel with the commoners? They might have to see or even touch someone below them.
(Sometimes attributed to differently: “A developed country is not a place where the poor have cars. It's where the rich use public transportation.” ― Gustavo Petro)
It's probably time to close that airport. It's too small and very inconveniently (for safety and security) located, even though it's convenient for travelers.
Which is why it will not close. It's easier for Congress members, senior staff, etc. to use rather than the drive out to Dulles of BWI. It's convenient for powerful people.
It’s convenient for everyone. Normal, local people (including myself) tend to strongly prefer DCA when a route is available in/out rather than deal with Dulles or BWI.