Also in the nets, the bowlers practice their bowling and the batsmen their batting. They will be too tired to have their full concentration if giving it their all during training.
I'm only talking about an extra say; 30 mins of batting in a full day of training.
How many hours per day do they train? It would be at least half a day I'd expect?
As a golf coach, one of the things we had to do with elite golfers was analyse their strengths and weaknesses and get them to pay more attention to those weaknesses.
A full-time player would typically practice for 3 hours, and play 18 holes - every day.
But, it's broken down into sections - 30 mins putting, 30 mins on chipping, 30 mins on pitching - and so on.
Then go and play 9 holes, and go back for a bit more putting, some driving, some long irons or whatever, then out for another 9 holes later...it stops the player from getting bored, and keeps them circulating through the various aspects like they would have to do on the golf course.
But, if the player is well above average in say; pitching - but cr@p at chipping - they may substitute half of their pitching time towards chipping, etc.
Surely (as a loose example) someone like a Glenn McGrath - who is already a fantastic bowler, can slot in a few extra minutes of batting with a batting coach, and drop a few minutes off the bowling practice which he already excels in?
All too often the problem is nothing to do with hand eye coordination, it is the mental side of it. Like Watson not being able to leave a ball alone in the last over before lunch, or Warner being more focused on moving off 49 than playing a ball on its merits.
My opinion on the openers (as a golf coach) is that they are in the team because they are already fantastic batsmen, so the problem is probably a mental issue, as you say.
I tend to agree that the change in format (and less test play) doesn't help their mental adjustment. They get used to scoring runs very quickly in 20/20, and then have to switch to "stay at the crease and plod along" Colin Cowdrey type cricket mode. It would be very frustrating and cause impatience, I would wager.
I think the problem has more depth to it though; off the field politics and so on can have a very large impact on a player's performance, and a few failures at the crease only compounds the mental state.
Those guys may need to spend time with a sports psychologist (if they don't already) like many of the golfers do to give them a consistent thought plan for each ball bowled.
