The Labour Party is currently thinking about a plan to make Council Leader elected by the Labour Party membership in some pilot areas, a move described by Newcastle's Nick Forbes as "probably illegal". He may well be right on that, but it is also worth considering how undemocratic and unworkable it would be.
Under the current system appointments and decisions are made in public by publicly elected people on the basis of published documents prepared by professional staff. They are trackable and the people making them are accountable to any member of the public. Of course, there are cases where the practice falls short of the ideal, but there are safeguards to ensure some measure of accountability which cannot be circumvented.
The proposed system would be that half a million Labour members (perhaps 1% of the total electorate), and probably a lot less, would vote in the Council Leader. No one outside the Labour Party membership would be allowed to know who was making that decision or why. The Leader would be beholden to these people who would be under no obligation to know anything about the operations of local government.
In my experience even quite long standing Labour members can be quite ignorant about how local government works and what is and is not possible. The recent example of regeneration in Haringay illustrates this rather starkly. This probably won't impact certain decisions. For instance any Council Leader who tried to implement an old style Militant mandate by Party members not to set a budget would just be removed from office by the Secretary of State. Similarly populist moves like cancelling contracts without compensation would just result in losing legal actions.
The real unworkable aspect would be any effort at transformative reform such as (for example) Brent Civic Centre, changing the recycling set up or large scale regeneration projects. These all take a long time to put together and involve complicated trade offs. Any of them might be subject to a populist campaign to veto them which could be used to attack a Council Leader in the way that Claire Kober was attacked. The result would be that Councils would effectively be unable to push such projects through, particularly if it meant working with partners (as typically happens in regeneration). That means that Councils would not be able to deal with major problems such as large sub-standard housing estates. Ironically, they would be forced into a position where they were just administering Tory cuts on behalf of central government _ precisely the opposite of what the Labour Left say they want to achieve.
You can get an idea of the frustrations that some Labour councillors feel about on this here.