The systema classes at my school. Are taught at full speed. They use replica weapons knives and guns but they show it slow speed and they progress until its fast. I have seen the guys that train this regularly for a couple years now, and they go all out.
But then again it all depends on the school and their insurance's. If you have two guys that actually want to be prepared they'll train hard and training hard will prepare you for most.
"you can protect yourself with the basics and forget the fancy stuff."
This is true. Basics are the best for SD. Most people who train MMA will do fine in a self defense situation. However, there are some things routinely trained in mma that really aren't necessary for the average joe to learn to defend himself, and a few things that just aren't included in most mma training that could be useful in dealing with an un-trained attacker.