It might work, but there are some minor differences of emphasis between the bodies which could transfer into internal wrangling. It is already difficult enough to ensure consensus.
For example, PPL/IR would probably like universal Mode S, whereas some AOPA members would find that untenable.
We work together - for example AOPA and PPL/IR are sharing much information in the IR NPA, and PPL/IR organise the seminars for Aero Expo.
I see no sign of imminent death for any of them; certainly the ones I am involved in are in rude health and fighting fit.