I'll counter the whole ASL notion that US tanks only rarely had gyrostabilizers. I bet all US tanks produced, at least from 1943 on, had them. First there is this 1944 Popular Science article that says so:
http://warfaretech.blogspot.com/2014/07/gun-stabilization-as-explained-in-1944.html Second, the 1943 TM for the M4 and M4A1 tank (TM 9-731A) says that the tank will have either mono-stabilizer, a modified-stabilizer or a dual stabilizer. it does not say "may" nor show how to check to see if there is one or any way to ID if there is one, but it does show how to ID the control boxes of the various types so the crew knows which one to have.
As to training, there really is not much to train on. One simply turns on the stabilizer. (I was an M2A1 BFV crewman and we had a stabilizer... there was noting to training on except to turn it on and ensure it was on.) The manual has just one page plus a few paragraphs on the next, of operating instructions (p 362) and most of it is on the pre-combat checks and setting the controls. The important check was to ensure enough hydraulic oil in the oil reservoir and in cold weather, to allow the oil to warm up. (and BTW it is simply called a "stabilizer"in the manual, not a "gyrostabilizer.")
I suspect why you do not read much about the stabilizers is that they were common parts of the gun system and no more thought was given to them. The exceptions may be when they did not function properly and thus get mentioned.
I've fired the gun on the BFV without stabilization and it makes it much more difficult to stay on target, even when stationary due to recoil. As mentioned above, the one thing the stabilizer really helps is laying on the target quickly when you halt. I watched a lecture by a guy who does the research for World of Tanks and who is also an armor officer in a the National Guard (and has deployed t combat). His research show the Sherman was about the fastest tank in WWII to lay on target and fire. This was due to the breach, especially on the 75,mm, the layout of the crew in the turret and the sighting system. i suspect, the stabilizer had something to do with this but is not mentioned because it is common equipment on the tank and expected to be used in combat.
As to maintenance. I would like to see the actual maintenance records of tanks with failed stabilizer vs. those that were operational. In other words what is the actual OR rate of the stabilizer? Does anyone know? One has to be careful with giving a disproportionate weight to anecdote... these have plagued the M4 series tanks for years and finally get disproved by good research and actual data. As to crews disconnecting them; why would they? You can simply turn the thing off. I would surmise that disconnecting them could cause further issues with the gun laying system. Again, be wary of anecdotes. The US Army in WWII was very good on reporting issues with its combat equipment. if the stabilizers were causing widespread problems, there will be official ordnance reports out there stating such.
ASL may have this issue backwards. From what I can tell, is that what should be done is at the start of a scenario all US tanks should roll a die... on a 6, they DO NOT have a stabilizer...