What evidence do you have that there is a causal inverse relationship between public sector growth and private sector growth? Isn’t it entirely possible that private sector growth has lagged because some third process has produced fewer entrepreneurs and fewer entrepreneurs results in less private sector growth? It’s possible that the relative difference in public and private sector growth is caused by fewer entrepreneurs, not the other way around. Basically, your argument is a classic case of assuming causality from a correlation.
A lack of private sector jobs can be caused by a lack of entrepreneur's. A lack of private sector jobs can cause a lot of people to be eligible for welfare. The government can then be incentivised to react to this by increasing public sector jobs, which at least makes people somewhat productive in theory while also giving them the means to provide for themselves.
I'll point out that none of the beliefs expressed so far actually contradict each-other. Less entrepreneurs could mean more public sector jobs. More public sector jobs could mean less entrepreneurs. Third order effects could mean less entrepreneurs as well.
