We get a few ego cases that have to "win" every time they roll or participate in a drill. One of the first things they do is let a new student roll with a senior student who really doesn't do anything but hang on and maintain a dominant position till they gas. Just too give a lesson in why it's a bad idea too muscle your way through. We generally do a best two out of three, but the standing rule is NEVER take all three taps. If you've got the first two let the other guy get some practice in and let him have the last tap.
This is very close if not exactly the type of technique focused training I am used to. The idea of going all out to submit someone is a different part of training, just like with different kinds of sparring. We might roll in class as you described bcullen, then at the end of class or after class we can have challenge matches where we go all out (in a controlled environment) to try to submit the other. Challenge matches are voluntary, often a person is pretty tired after three or four matches so you get pretty aggressive to try to make things happen faster, IME. Half-speed practice is more of a drill against resistance than trying to win or lose. What you described slideyfoot is one way it can be done. One drill is to try to slow down the pace when in an advantageous position. Much of BJJ is learning how to keep the dominant position once you have it. So the person in the dominant position should learn how to use technique over strength and speed. On the other hand, the person in a disadvantaged position needs to try to speed things up so that they can break the timing and cause the other person to make mistakes. One of the methods of half-speed or lower intensity rolling is to have the one with an advantaged position stay at half-speed and use technique to keep the advantage... have the opponent try resist up to full speed to try to get out. In other words, low intensity until one or the other gains the advantage, then the disadvantaged person is allowed to resist at a higher intensity. One point, just because you want to slow things down when in a dominant position does not mean you do not protect yourself. The opponent is going to try to go faster and use more strength, so trying to slow down the pace (e.g. half-speed) does not mean you are not defending yourself against full speed attacks on you.
I think a lot of the way the art is marketed and the MMA concept has a lot to do with this problem. How many times have I heard BJJ is the dogs B****ks because it is trained with your opponent fully resisting you. This leads to some Idiots believing that all drills are carried out full on and that leaning with your forearm into someones nose is OK to get the opening for a sub because thats what the BJJ guiys do in the UFC.