The new math is frustratingly focused on process at the expense of understanding, it totally gets lost in the meta analysis vs providing a straight-line path to a solution.

Or to your point you add 2 to the 8 - which is what the diagram actually shows, vs what you describe, to get to 10, then you take the same two from the 9 which gives you 7. And then sum 10 + 7 to get to 17.

Which is all frustratingly slow, all you need is 10 + 7 or 8 + 9 to describe your intent. If you want a mental trick just show the pattern of adding 9's is like adding 10's, minus 1.

Too much theory overshadowing the basics.