Why do we give homework?

I have been pondering the aspect of homework the last little while. Particularly in mathematics. True some amount of repetition is required to obtain a skill but how many students actually care enough to do the work to improve their mathematical skills. The ones that don't need the practice are the ones that complete the assignments, and the ones that do need the practice rarely, if ever, have it done. Homework is done by those that benefit the least from it. Now I can try to entice them by saying there will be a homework check but even that is flimsy and superficial. I want them to do the work because it will help them learn and achieve success in the class and thus, encourage life-long learning. By attributing marks we are just encouraging students to be externaly motivated by marks which, in my humble opinion, is what holds students back from truly learning for the sake of learning. I think we have to look at the facts, students are a big part of the working class. Many have "part-time" jobs that take up to 30hrs a week of after school time. If you add in an after school sport or activity when is there time for homework? I think the idea that there has to be homework has been ingrained in our thinking of what school is. "What? You don't have homework?" Some may feel that if there is no homework being sent home then there must not be any teaching going on. In fact shouldn't we get through enough material in a one hour class period which would make practicing at home redundant? I know at times homework and letting students start their homework in class is an easy fix for poor planning and poor classroom management. I think we need to get away from homework and focus on assessing students. I would rather spend time on assessing then checking if the class did 1-30 odd from yesterday assignment.
I can feel that this is going to be an ongoing debate in my head I start my teaching career. If I come in with the notion that I don't want to give homework who will take me seriously? After all, I am just a new teacher...what do I know?