I absolutely agree that this is a question worth asking. I have only recently come to realize that all of the abstract stuff I've been learning for the past few years, while interesting in its own right, has concrete applications in physics as well as in other branches of mathematics, none of which was ever mentioned to me in an abstract algebra course. For example, my understanding is that the origin of the term "torsion" to refer to elements of finite order in group theory comes from topology, where torsion in the integral homology of a compact surface tells you whether it's orientable or not (hence whether, when it is constructed by identifying edges of a polygon, the edges must be twisted to fit together or not). Isn't this a wonderful story? Why doesn't it get told until so much later?
For what it's worth, I solve this problem by getting a different book. For example, when I wanted to learn a little commutative algebra, I started out by reading Atiyah-Macdonald. But although A-M is a good and thorough reference in its own right, I didn't feel like I was getting enough geometric intuition. So I found first Eisenbud, and then Reid, both of which are great at discussing the geometric side of the story even if they are not necessarily as thorough as A-M.
As for the first question, I have always wanted to blame this trend on Bourbaki, but maybe the origin of this style comes from the group of people around Hilbert, Noether, Artin, etc. Let me quote from the end of Reid, where he discusses this trend:
The abstract axiomatic methods in algebra are simple and clean and powerful, and give essentially for nothing results that could previously only be obtained by complicated calculations. The idea that you can throw out all the old stuff that made up the bulk of the university math teaching and replace it with more modern material that had previously been considered much too advanced has an obvious appeal. The new syllabus in algebra (and other subjects) was rapidly established as the new orthodoxy, and algebraists were soon committed to the abstract approach.
The problems were slow to emerge. I discuss what I see as two interrelated drawbacks: the divorce of algebra from the rest of the math world, and the unsuitability of the purely abstract approach in teaching a general undergraduate audience. The first of these is purely a matter of opinion - I consider it regrettable and unhealthy that the algebra seminar seems to form a ghetto with its own internal language, attitudes, criterions for success and mechanisms for reproduction, and no visible interest in what the rest of the world is doing.
To read the rest of Reid's commentary you'll have to get the book, which I highly recommend doing anyway.
