Lisa, it’s a pretty good libertarian argument, so long as the money raised by taxing these pastimes is used to reduce taxes elsewhere.
You also ask “if we really want to set up state-regulated brothels” to which the answer must (if prostitution were legalized) be yes. Libertarian absolutists might not like it, but given both the high risk of exploitation in this business and the obvious health considerations, I would think that this is an area where the state does have a legitimate interest in regulation (this doesn’t mean that it has to run the brothels itself, of course). It’s worth adding that the fact that legalized prostitution would be easier to regulate is an excellent pragmatic reason for legalizing this trade.
You go on to argue that raising revenue from these activities will cause the state to lose legitimacy “amongst that part of the citizenry that cares about morality” (as you define it). That might well be true (if not necessarily logical; better to tax the “immoral” than the “moral,” I would have thought), but it can be a dangerous line of argument to follow. There are a good number of good people who regard war as morally wrong, but is that a reason to scrap the army?
Finally, I think we have to be careful about categorizing smoking tobacco and promiscuity as activities “that we all regard as dumb, self-destructive, and costly” (my emphasis added). In the case of the latter it rather depends on the individual. Promiscuity is disastrous for some, fine (and maybe even profitable!) for others. As for tobacco, well, it’s certainly costly (thanks to the government), and in most cases it is, if pursued too long, self-destructive, but I’m not so sure that it’s always “dumb.” There are some who believe that a shorter life made sweeter than its tobacco-free alternative by smoking is a preferable option. That’s not my view, but I wouldn’t describe those who have thought it through and come to that particular conclusion as “dumb.”