how can Nikah mut'ah be used as cover for prostitution when it requires 3 months waiting period?

I am not certain if it is or is not in reality used as a justification for classical prostitution amongst the Shia, but the wikipedia article Prostitution in Iran - Wikipedia claims that to be the case. Well, the article on this relationship says that the woman has to observe a waiting period of 3 months called Iddah - Wikipedia after the divorce. So I can understand how this type of arrangement could be used for a medium term “sugar daddy” relationship, but how can you have regular prostitution with waiting periods of 3 months between clients?

Incidentally, this link Yahoo | Mail, Weather, Search, Politics, News, Finance, Sports & Videos claims that they even had some law in Iran legalizing brothels based on this notion. In general, google searches for “Iran prostitution mutah” are returning lots of hits, suggesting that Wikipedia article is not just blatantly wrong.

AFAICT, you don’t. Women in Iran who practice what we think of as “regular prostitution”—frequent brief encounters with a random variety of clients—don’t bother with a sigheh or “temporary marriage” contract, and don’t observe 'iddah. Consequently, they are violating the law.

Sigheh is condoned or even promoted precisely because it provides an officially tolerated alternative to “regular prostitution”, which is considered bad from the standpoint of public health and public morals.

Generally, the people who say nikah mut’ah is just cover for prostitution are Sunni, who frown on mut’ah, and use the fact that the practice exists to criticize the Shi’ites for immorality.

A study of prostitutes in Lahore in the 1990’s found that most of them were (or professed to be) shia. Of course it (being Shia or Sunni) is not that big a deal here (loser secetarian groups nothwitstanding).

Isn’t Pakistani Punjab largely Shia itself, though? Is there a higher percentage of Shia prostitutes in Lahore than the percentage of Shia in Lahore?

Of the seven Pakistani provinces and territories only one; Gilgit-Baltistan is majority shia. However there are major shia minorities all over Pakistan and Punjab is no exception.

As said before, the divide is not as pronounced within Pakistan and you get Shia and Sunni people in the same family; mine for instance.