I feel there needs to necessarily be a separation of the doing of mathematics and the teaching of mathematics in these kinds of matters. In the teaching of mathematics, especially in the more 'abstract' areas, there is not nearly enough driving of intuition, and the 'problems' students are given often are unrelated to the 'problems' the theory they are learning about was created to solve. Pushing things in the concrete direction is probably the right direction for pedagogy.

But in the doing of mathematics is where I think Arnold is looking back at the past too romantically. Prior to programs like Bourbaki, the lack of unity in mathematical notation, definitions, ideas in methods was very present. Often if you were not a student of one of the masters of the time, you would have an incredibly difficult time understanding their work. The tradition that has lead to an 'over-abstraction' of things, as Arnold would have seen it, also lead to a much more widespread accessibility of contemporary mathematics. when you can count Kolmogorov among your teachers, this is less relevant to you. But for the 'unwashed masses' of mathematics this has made a world of difference.