I don't see the shame if you are a single prominent person (though things get VERY sticky if you're married or have a long-standing relationship) who has their picture on a dating site. Like everything else, it depends on what standards you have, and how careful you are in selecting your mate (for example, making sure they're not just marrying you for your fame, money, or social status).
And frankly, I wouldn't accept that as an excuse if I ever heard it. If you're too famous to merely show me your picture, then I'm too poor/unknown/low-class to date you.
The reason I got was that all info out there in the media can be used to undermine their professionalism, or ridicule them by competitors or even colleagues...which I agree. Also the reason a lot of them are not on social sites like FB, Twitter, etc etc. But as long as they are able to show it offsite, it is reasonable enough. There are however, some who even continue to give you fictitious info and pics....and those are ones to beware of!