I actually think it makes perfect sense, once you reached a certain age you will feel more anger at the world than you have as child, training a frustrade (or nearly) teenager in the way of the force is dangerous!
But ignoring them and letting them do whatever with all the power they have is fine and dandy? Especially for someone who's clearly been described and understood to be one of the most potentially powerful Force users ever conceived? No, that really doesn't make any sense at all.
Also, that sort of thing happens all the time in the real world, particularly in martial arts, ascetic monks, certain fields of the military and government like the Secret Service, and other areas that require a high degree of discipline.
You don't spontaneously become unable to learn to control yourself after you hit a certain age. If anything, you become better at it because you know
why you're being trained to do it and how important it is to learn.
It was just a really terrible idea Lucas had, and it shows.
Who did the Sith ever "teach how to wield the Force at an older age"?
I mispoke. They have no problem teaching others the way of the Sith for people over the age of 10 or however young Anakin was in the Phantom Menace (he certainly hadn't hit puberty yet and wasn't much older than any other "youngling" -- what a horrible choice of words -- shown in the movies). As opposed to the Jedi Council who thought he was too old to train as a Jedi, not just how to manage his Force.