Is this example really illustrative of "the state" keeping "precious resources (from) falling into the hands of too few in a society"...??
I think this is a fair criticism, but my point remains. The New Jersey Law Against Discrimination grew from inequalities (perceived or otherwise) caused the state to change the rules on what could be done with property. The same was done with the Civil Rights Act, and the ADA. Generally there are carve outs for private clubs, but there needn't be, as is the case with building codes, rules about what pesticides and herbicides may be used, etc.
My point isn't that I think a mob with pitchforks is going eventually going to demand access to Augusta National, but only that the leviathan is the ultimate arbitrator of property, and folks should be careful in their (typically here, inherited) stewardship, because even something as simple as inequality in public accommodation could cause a major changes, as it did in 1964 in the United States.