I think you're right about the importance of understanding all of the reasons why people don't vote. It's true that some of those reasons have nothing to do with the voting system. However, it is clear that quite a few of their reasons are indeed related to the voting system.
You raised what I think is an important point: we cannot expect that changing the voting system will meet everyone's needs or fix all of the problems with our democracy. There are other things we can do to increase voter turnout. I agree with you on that.