Ideal trainer versus standard puzzles

Moistvon, you're forgetting that engines are programmed to win, and they don't "know" who their opponent is. So they don't offer a draw at move 1.
Yes, computer evaluations also use global concepts like "space", not just discrete calculation. We agree, however, that an advantage in space, all else equal, increases chances of winning. One can say the same about material advantage, coordination of pieces, and any other "advantage". Ultimately pieces will be captured or the king checkmated, which you can call "tactics" if you like. However, overwhelming power seizing material or squeezing the king can be straoghtforward at that point, whereas "tactic" implies some finesse or skill.

@nayf Of course, calculations are important. Neither did I say, they are not, nor that humans cannot do any calculations.

But: If strategy was some kind of very deep AND complete calculation, then:
1st) It doesn't help you, if the computer showed you the tons of possitions it has evaluated, to find the strategically best move
2nd) You can train it with the normal tactic puzzles, but you will never reach the abilities of an engine.

If strategy was something different, which uses some kind of approximations or shortcuts for long calculations, then the computer (at least the classical stockfish et. al. types of engines) are not better than humans.

Of course humans will never again reach equality with engines; on the contrary, the gap will continue to widen as programs improve. I don't follow your last point. Computers are better at strategy, tactics, checkmating, end games, middle games, openings, and everything else. They also have 3 other advantages that a GM who played them remarked: they never get tired, they are immune to psychological tricks or pressure, and last but not least, they nev0er have to pee.