I've responded as follows:
It's an interesting idea from Lynne , but ....
I have to say that I thought as party members we elect the leader of our party, not the leader of the parliamentary group (though obviously the two posts are normally combined) My feelings are that once councillors are elected, they should make up their own minds on issues (either individually or as a group) and not follow the instructions of the wider party.
Councillors shouldn't follow party instructions on a planning application or other agenda item, I don't think they should do so when the agenda item is the appointment of group leader.
Obviously a council group and local parties should co-operate as much as possible, but party instructions should never penetrate into the council chamber.
PS : I'm not sure how it would have worked out the two times I've been elected group leader on Rochford DC. The first time nobody else wanted the post (we were the largest group on the council then). I nonetheless asked for a secret ballot of all the councillors to confirm my positon (which I'm pleased I won).
The second time was when he had been reduced to just four, and nobody else wanted the post either (the other 3 being newly elected).
The question our group had when we became a majority was - when you have chosen your leader, does he or she pick who chairs which committee (as a PM selects a cabinet) or should the group vote on it?