Actually some proposals have been floated in the past where each Chinese, gets a dividend cut from each SOE.
This would ensure continuous bottom-up public support for SOEs, accelerate income growth, and enhanced monitoring of SOE's financial and competitiveness performance ("we are talking about my money here!")
Of course as a counterpoint, it can be argued that this already happens in an indirect way by the SOEs funneling money to the Gov as taxes, or by supporting unprofitable projects for offering public goods.
It's a complex issue for sure, however I quite like the argument that it would ensure bottom-up support from the public. Everyone is aware of the private businesses hiring so many people and contributing so many taxes, they are more efficient etc, but sometimes it's difficult for the average Joe to understand the value of SOEs.
In the beginning it may not affect much, but who knows if in the future, public sentiment turns against SOEs? Such a measure would be a concrete real world benefit that every single person could enjoy and experience personally.