Personally I can't see it being ditched-tweaked, perhaps-anytime soon.
The general thrust of your comments regarding Bidline is correct - it is cheaper and more efficient than some other systems. However, it is constantly being tweaked and changed as changing needs and desires in the workforce occur. When BA changed from a system of allowances, based on destinations to one based on time away, the patterns of bidding changed dramatically and Bidline was changed to ensure work coverage. There is some disquiet amongst junior pilots at the moment due to stagnation and the subsequent problems of being very junior for a long time. I doubt this will lead to a significant change in Bidline but there are several discussions on the BALPA forum about it.
Bidline is a constantly evolving and changing tool, it is not a set of rules that are cast in stone that has not and will not change. The pilots "own" Bidline as a joint venture with BA and both parties can and do seek changes in the rules as the circumstances change. I do not see Bidline disappearing in the near future but it will evolve and change.