I think we should look at this from 2 different view points. First, from the LEO standpoint and the second from the civilian viewpoint. Now, regardless of which one, in either case, I don't feel that being on the ground, especially for an extended period of time, is wise and I don't think that I should have to list the reasons why.
For the LEO, regardless of how he got there, either by taking the bad guy down or being pulled down, the idea is to control the bad guy. Also keep in mind that the bad guy is probably going to be trying very hard to reach for the LEOs weapon. I would think that at that point, getting up is more important then staying on the ground.
The the average Joe who is in a fight...like I said, learn some basics, and try to get back to a standing position. If a submission presents itself, and you feel confident in taking it, fine, but I would not stay there on purpose just for that goal.
And I know this always comes up in these discussions, and both sides of the fence argue their point, but I feel that the environment should also dictate what we do/don't do. I havent seen a BJJ fight yet, where someone that is in the circle around the people fighting, jumps in to help. That is a mutual agreement. Yet in the real world, there is nothing to stop someone from joining in, kicking your head, punching you, or doing anything else.