The prevailing narrative seems to be that it was ye olde church/temple/synagogue that selfishly imposed a tyranny of restriction with regard to women's chastity without heeding the desires of the governed, that this had nothing to do with men's own preferences (with a close second being that it was a function of patriarchy, in which case presumably there is a corresponding acknowledgement that yes, that is indeed what men prefer).

So which is it? Assuming availability/practicality/social stigma is no obstacle, do men prefer virgins/chaste women for marriage?

Of course, there is a great deal of stigma against such a preference, to the extent that there is some non-zero portion of men who labor (sometimes tirelessly) to suppress their preferences as a result of societal narratives condemning the preference. Presumably they would be counted as having the preference.