How would that work, then? Removing them kind of defeats the purpose of having them to begin with in D.C. since you can't bring them with you. Why wouldn't they follow you? They're your companion, after all.
Also, realistically speaking, a companion is a person with their own life, not some robotic slave that is forever attached to you every minute of the day. I would think that in 9 years' time, maybe your companion from D.C. might have been having a night on the town by themselves when Benny and the Jets attacked you. Even more so, maybe Benny and the Jets waited for the night when you didn't have your companion to attack you, maybe even they were the reason your companion wasn't there (slipped a mickey in their drinks, lofted some tail on the strip in their direction for a night, etc etc, could be a million things).
It only makes sense, then, that your companion is there when you wake up. It's what friends are for, after all. I mean, you might have come to Nevada with your companion, and then 8 years ago, your companion split to do some of his or her own things, and then hearing that you were shot, he or she came to find you again, so once again, you would still wake up with your old friend there.
That's how I see it, at least. I, for one, would be very annoyed that my companion(s) aren't there when I wake up. What the hell kind of companions are they, then?