In Judo the rules are geared to maximize stand-up fighting time. If a failed throw attempt occurs and things progress to newaza (or ground work), Judo players have a very short time to show that they are progressing before a ref will stop the match and return both players to their feet. Effectively this means that you can turtle up in a ball or lay flat for a few seconds and the ref will stand you back up. The result is that when grounded you don't have to work to stand back up yourself as the ref will do that for you.
In BJJ, once grounded, it may be to your disadvantage to stand back up. A player may completely disengage his opponent and the other opponent does not have to follow him back to his feet and can sit on his bum to reengage. Also when you stand back up if on the way up you get tripped you risk loosing 2 points on the takedown, even if you only returned to one knee up. These rules are geared to create a safe haven (or at least a safer one) for the bjj competitor.
In MMA, however, the importance of standing back up once grounded has become very apparent. The competitor on the bottom does not want to remain there, does not want to take heavy damage in strikes, and so they learn systems and sequences to use the cage etc to return to their feet. Of course it isn't as though Judo and BJJ experts don't know how to return to their feet in a match, but I believe it isn't a primary skill emphasized to competitors because of the nature of the rules of competition. If we are to train our grappling with martial principles in mind, I think that the ability to return to your feet when desired is of paramount importance.
Here is a simple video I found on line on how to return to your feet when you have someone in your guard.