That's pretty much tautological

Not really. There's a third option - that forbidding things with no evidence that this will improve the world does not correlate either with increased fun or decreased fun, so that we could pass laws on a whim without concern. My claim is that this is not the case - that there is a correlation and the correlation is negative.

What you really need for this argument to work is a way of showing that people attach intrinsic utility to increased latitude of choice, which in light of the paradox of choice looks questionable.

Ehh... I am confident asserting that prohibiting things merely on the basis that people are often happier having fewer choices will not in fact general to increased levels of fun. Having fewer choices might make people happier, but being denied choices by their government probably won't - and I'm certainly not optimizing for happiness, in any case.