Investigations cost money. They cost time. They use resources. Unless there is a valid reason to believe that Senator X really does visit prostitutes, there are better uses for that money and time and those resources than to conduct an investigation for no reason. Now, the people who are conducting the investigation may be wrong, but they'd be, to be blunt, stupid to conduct such investigations without reason.
And if there is a reason to believe he does, and the investigation shows that he doesn't, then that is to the Senator's benefit. If he does, then he's brought the harm down on himself.
Now, I'll be honest with you. After seeing your definition, I can think of one individual, who is very much in the public eye, who has been investigated in such a way that might be considered punitive by your definition, and whose reputation has suffered as a result. However, it is also true that the faction who conducted the investigations in question has suffered a very serious loss of credibility.
And here's another thing. Look up at the paragraph about. I can think of ONE individual. ONE. ONLY one. Now, have there been others? I'm sure there probably have, been occasional other instances. But it happens FAR less often than I think you are imagining, and the stakes in the only case I can think of were very, very high. What's more, I think in the long run the folks who conducted the investigation are going to suffer just as much as their alleged victim.
It doesn't happen often because the loss of money, time, resources AND CREDIBILITY are just too high.