I think it is a thankless task and difficult to make any real difference unless you are a member of the ruling party and in the cabinet. Individual independent councillors are unlikely to have any real influence unless the council is 'no overall control'.
In the case of the library I don't think any of our councillors attended the mayor and cabinet meeting and certainly didn't choose to represent the views of their constituents. The decision had already been made and they knew there was nothing to be achieved by opposing the mayor's inevitable decision.

Much of the work of councillors goes unnoticed, it is about issues for individual families, such as housing problems, rather than the big issues. And when council budgets are being cut every year it is very difficult for the council or councillors to make a positive difference, the best they can hope for is to limit the damage. I don't see why anybody would want to do that job at the moment, unless they saw it as a route to bigger things in their political party, or took pleasure in reducing the role of councils in the community.