I think this whole argument implies an interesting normative method for evaluating government policy. Your implication seems to be that restricting some freedoms for some people ends up producing an overall increase in freedom relative to no restriction. The obvious crimes come to mind first but the framework could be applied elsewhere. Take copyright for example, do I have the freedom the control my own creative work however I like, or does the freedom not to have to constantly worry about the source of media outweigh the freedom to control my creations. More succinctly, in a world without copyright are we more or less free? It's not obvious to me.

Singapore is a case in point, freedom not to be caned for minor infractions vs. freedom to walk around relatively safely in a high density metropolis. Again who is more free is not clear.

I think you are wise to suggest there might be "maximal" achievable liberty. Does the culture of society affect the attainable liberty opportunity set? It seems like it must.