"I think where math goes wrong is displayed beautifully in the rational expressions units (I didn't go to the original link, so forgive me if I'm entirely redundant here). When I was building the math content for the ed s/w company I was struck that nowhere in the chapter where students learn to simplify fractions involving a polynomial numerator and a polynomial denominator (tough stuff when you are first learning it) nowhere in the textbooks did they tell the student WHY. Why do all this hard work? What is the answer that we seek from all this?"
What do you think are the answers to your questions?
One thing that was quite easy to do is to set the rational expression equal to something and solve for one of the variables. We did a lot of problems where there was only one variable: (x^2+9x+20)/(x^2-25)
In motivating them you don't necessarily have to give every reason to learn something, just reason enough to buy into what you are trying to teach them.
But the motivation for solving complicated rational equations does not come from word problems. The word problems for this topic involve very simple rational functions. My point has been that the motivation for studying and doing much of mathematics ought not come, solely, from practical word problems.
I agree with you that you (we) shouldn't feel the need to have a one-to-one mapping between problems we solve and word problems. Even in elementary physics you could argue that the word problems in many cases aren't practical, but we teach it to teach the flavor of the approach; the attitude of how we attack problems (or, less poetically, what exactly we mean when we say "cause and effect").
That said, the motivation is still greater when the students see some hope that what they are learning is meaningful.
What that motivation is depends on the level of the class. For algebra 2, it might be "we learn to manipulate rational functions because it gives us a tool to understand (or solve) a certain class of problems. Someday you may own a business where you have to worry about the average cost of something that depends on things that change alot, or variables as we call them. And you know what an average is: it's the amount of something divided by how many there are. Well if your amounts are represented by an algebraic expression, and your total is represented by an algebraic expression, then the quantity you will be interested in will look something like this (writes a rational function on the board). Now, what the fuck do we do with this?"
What do you think are the answers to your questions?