This isn't exactly a new idea. Private clubs were banned in the Roman empire specifically because of the risk of collective action (they didn't want clubs to be the seed of a rebellion). We have correspondence from a governor to the emperor where the governor says (paraphrased, obviously), "a bunch of the men locally have put together a firefighting group, so if a building catches fire everyone shows up and helps put it out. This seems like a decent idea to me, is it OK?" The response is "absolutely not".
The government is not so much concerned about desire to "fix" things as people's desire to politically organize in ways they don't control, hence the perhaps more surprising aspect of the earlier post: they're less keen on individuals organizing rallies in support of a leader than they are on those individuals voicing a personal criticism of that individual.
Reading on what demonstrations of popular support for specific figures within a notionally unified establishment became during the Cultural Revolution is helpful in understanding the present leadership's paranoia here.