For what its worth I do believe shrimping is a good warm up, and some of the other line drill movements people need practice on.
When you only have an hour long class wasting a lot of time on this stuff sucks. A 15 minute warm up is a 25% of the class, the warm is suppose to be like an appetizer its to get your body ready to eat not fill you mostly up.
Shrimping is something that lots of people think they've mastered when they haven't. I took a self defense course in college taught by a good judo coach, and he had us shrimping. Man, you shoulda seen it. People Pac-Manning side to side but staying in the same place, moving along by bridging back, all sorts of weird stuff.
If your brain's too tired to remember what you're learning, buy a notebook. Buy a notebook anyway. Write things down. Make drawings and diagrams. The next time the topic comes up in class, refine your notes.
A hard work out not only tends to take the strength out of techniques, it also tends to take the edge off the folks who are unable to relax at all and have a tendency to hurt their training partners "by accident".
Absolutely have a notebook. I have 2. One for scribbling things down on the spot, and another for a 2nd draft that's more legible and organized (and with cool drawings!).
You know that repetition is the key to learning, right? And most of the stuff you do is important in rolling.
As many folks pointed out, if you are gassed you make a certain type of decisions, those are usually your 'fall back' move. The ones you drilled the most and the ones that you know the best/feel most comfortable with.
The other point, that was already mentioned, most of the warm up stuff is crucial to JJ. Shrimping/hip positioning being one of the most underrated (by beginners, heck even intermediate guys) skills in all of JJ. So doing it over and over and over you learn to do it for when you need it. If I am fucking up in rolling or drilling, first thing I check, is my hip in the right place (too high/ too low, too much in, too much out, blocked etc.) most of times this already fixes a big part of the issue.
Would I like training to be different? Sure I would.
If you ask me I would do a 5/10 min. to stretch warm and then drill technique (3 max. best attack/move - counter - counter counter) and then roll the rest of the class. I am working out on other days/times. But Jits here in Brazil, since you specifically mentioned it, is not any different then from JJ in the US or most likely where ever you go. You do the warm up, you drill, you roll. I have been to more than 15 schools in various countries from different coaches and such... everywhere the same. Warm up, drill, roll.
One could think there is a reason for it....
While I agree that grip fighting is important, I would never drill it. Grip fighting will **** up your fingers (I guess Judo and Jits folk will agree with me here).
One of the nicer drills that will get you warmed up is one I did, heck knows where and when, that is based on side mount. Bottom does everything to get out, top guy only is allowed to pummel in/under and switch base, no subs, no cross face no NS.
This is a super nice drill and it will kill you. Love that one!
Yeah, the best school I have gone to by far use to warm up a lot by doing something similar rolling just for position.
They also use to do a 10 round Monday night class as well and always had open mat after class. Man I miss that place.