EII,
As things stand now, the private clubs cannot form their own league and will have to co-exist with the government clubs and gradually work their way to dominate and take over the LMC (which is strictly not a government-sponsored body and hence doable).
It is going to take time which may discourage many investors from going into it. Even getting into the NPFL will take time because they have to start from the bottom and compete with other bottom teams like the blank shooters (

) unless they are able to buy over an existing club.