But yes, the Conservative party is in a very odd place. I often use the analogy of Jeffrey Archer who was also very popular with members. To Thatcher's credit she knew that but kept him close whilst making his actual power worthless.
Unfortunately Cameron and May weren't Thatcher who irrespective of your political views was a formidable politician.
One of the things that made Thatcher a formidable politician was that she picked her ministers on competence. Her cabinet always had a hard core of people who weren't hard core Thatcherites - early on it was Carrington, Heseltine, Pym, Prior and Walker; later it was Major, Hurd, Clarke and Chris Patten.
And if you were a Thatcherite, your views didn't matter if you were incompetent (Moore) or a transgressor (Parkinson), you were out the door. How very different from the current cabinet, where competence is almost seen as a disadvantage and where members walk a very dodgy path.
It's not a good way to govern a country.