You will find a lot of that at any 141 school. In order to get the ratings in the minimum hours, you have to have a good instructor and be somewhat of a 'natural'.
I would often complete lessons with out actually doing everything that was listed, because it was impossible. You can usually still find the time to make things work out by focusing on a few task on every lesson and having the student practice the maneuvers multiple times, instead of having them do an unreasonable amount of maneuvers once in a half assed fashion so you can cram it all in. For new instructors, it takes some time to figure this out. You also risk being called on the carpet for 'completing' a lesson without actually covering every task. I always told my students what I was doing and would also tell them that if the lesson was supposed to be 1.2 hrs and we needed to take 1.5 to get the lesson done, I would do it. In the end it is better (and cheaper) to spend an extra .3 to get something down than have to unsat the entire flight.
I do know several instructors who had retarded students who would watch their hours like a hawk and would bitch and say that the last lesson was .1 over, so the next lesson would have to be completed .1 under what was called for. It probably cost them more in the end.
For instrument work, there is no reason to have to actually introduce a task in the airplane without doing it in the Frasca first (or even better on Microsoft Flight Sim). Since DCA has these, they should be using them. It is much cheaper to learn in the FTD than in the airplane. There were some lessons in the FSI syllabus in the beginning of the instrument syllabus that introduced task in the airplane first and I simply did the lessons out of order, so it was always learned in the Frasca first. I would also not let my students go to the Frasca until they could intercept and track on the HSI, OBS, and RMI on Microsoft. It did not have to be perfect, but it was a waste of money to put them in the Frasca if they did not really know what they were doing.
For your diversion example, they should have briefed you ahead of time and had you do one on the ground, while not flying the airplane. Then after the first diversion if it was a problem, they should have had you do multiple 'practice' diversions again, while on the ground. They could also help you prior to the checkride, as once you know what flight plan you have to prepare, you can usually make an educated guess where you will be diverted to. The checkpilot usually only has you do the first few checkpoints, then gives you the diversion, which is usually not that far away. Sometimes this helps the student think ahead.
This can be one of the more difficult maneuvers for the private checkride, but can be much simpler than many make it. If you think about it, most class D airspace rings are about 8 miles across (A class C ring is even better). You can use this as a scale to estimate your distance to a diversion. You can use the rings around VORs to estimate a heading. Most trainers go about 2 miles per minute and eat about 10 gallons per hour. You can do the math in your head and come suprisingly close to the answer people struggle to get using their plotter and E6B while trying to fly the plane at the same time. I would also argue that you should not be trying to read the AFD while flying. There is no reason for it, and it is much safer to be looking outside. But, I also feel the same way about those VFR flight plan forms. I would rather have my students looking outside than trying to fill in little squares every time they pass checkpoints that are 10 miles apart. You should know about how long it should take you to get to key check points before you takeoff, and should keep track of your progress, but it is often taken to an illogical extreme.