In theory, training against engines offers several important advantages compared to other training methods such as studying books, or even playing other humans, at least under typical conditions (online / competitions).
Let's look at the four pillars of learning, as explained by Stanislas Dehaene:
Attention – you can't learn without paying attention. Specifically, you should be paying attention to precisely the aspect of the skill you're currently trying to learn. Against computers you have the ability to choose exactly what to train, e.g. a specific opening or endgame.
Active engagement – to learn, you need to perform the skill you're learning. Just studying books or watching videos doesn't cut it. Even solving puzzles doesn't really emulate the conditions of actual play. Playing against computers let you actively participate in learning, while avoiding distractions like competition.
Error signals / feedback – the brain doesn't learn without an error signal (note however that an error signal can exist without an error – uncertainty when answering correctly is sufficient). It is also known that the faster the error signal appears, the stronger the learning effect. Preferably, we should get immediate feedback after each move, on whether that move was good or not. Playing against computers, rather than just analyzing with them, allows such feedback.
Consolidation – repetition (with sleep in between) is the mother of all learning. A serious problem with playing other humans is that situations typically don't repeat very often. You might get a certain endgame that you need to practice only one time every several hundred games. This limits your ability to repeat the knowledge at set intervals (spaced repetition learning). Against a computer, you set your own schedule.
Give these benefits that are almost impossible to achieve while playing against other humans, why aren't computers widely used to practice against?
The answer appears to be: engines don't play (or think) like humans. Anyone with some chess experience who has played one knows this. Engines manage to combine crushing tactical accuracy with really basic mistakes that often seem to happen out of pity. This takes away the fun from play and makes it less realistic.
Moreover (as you mention), when used for analysis, their thinking process is often hard to decipher for a human. They call things mistakes due to some obscure engine line that a human opponent would never find. This is an instance of crying wolf – soon your brain will start to ignore the feedback from the computer because it's not intuitive and not adapted to your own level.
There are attempts to solve this, and make computer more suitable training partners & coaches for humans.
Some interesting examples:
Maia chess (e.g. https://lichess.org/@/maia1), is a bot based on a neural network trained on human games, binned by rating. It accurately represents some typical characteristics of humans. However, it appears to do no "calculation" on moves and as such miss basic tactics.
DecodeChess (https://decodechess.com/) tries to overcome the engine's limitations with regards to explaining moves. It analyses games and provides an intuitive list of descriptions of the benefits and problems of a certain move.
Noctie.ai (https://noctie.ai) is a humanlike chess AI that can emulate human play from beginner to master level (including calculation, realistic move timings etc.). You can set Noctie to play certain openings / endgames, etc. A strong feature with regards to the four pillars of learning is "Live Insights" where every move you make is instantly color-coded depending on the quality of the move as evaluated by the humanlike AI. You also get flashcards from your mistakes that you can practice with spaced repetition learning.
If / when these tools become mature to offer effective practice of all parts of chess skills, I think we'll have a situation where we play other humans for fun or competition, identify weak areas based on our results and then predominantly play against computers to practice those areas, perhaps under the guidance of books or other human-made content that tells us what kinds of situations we should practice against the computer.