I don't think that's really true. The book itself puts it much more simply and directly, at the very beginning in 'Preface for the Instructor':

"You are about to teach a course that will probably give students their second exposure to linear algebra."

Axler tries to teach students how to understand linear algebra.

If all that you want to do is use it, the prospect of that understanding may not be very motivating.

My point is that the comment that you quoted from the preface in no way changes the fact that the book's point is to convey an understanding of linear algebra that is primarily of interest to people going on in math.

Now I happen to think it is the right way to understand linear algebra and is how people in other fields should think about it. Because it is easier to figure out again if you've not done it in a while. But this point of view is primarily going to motivate would be mathematicians.

Sure, but the topic is 'Given Strang, what's the deal with Axler'. It's a perfectly sensible question in its own right.

It’s certainly not aimed at numerical analysis students, or engineering students, or physics students. (Which isn’t to say that those students can’t take pure math courses if they want.)