I have been told that Ueshiba did no warm ups in the class - he expected everyone to do their own warm ups before hand.
The problem is nowdays that we expect everyone else to be responsible for our training.
What I think is best is to get the mats out as quickly as possible and allow 5-10 minutes at the start to let people arrive AND to let those who need to warm up more to do so. Then a BRIEF warm up doing a general coverage of the body is done.
People require different amounts of warm up for different parts of the body (I used to have elbow problems and press-ups were the best way to warm up my elbows before class).