It's not just that someone might have to deal with an overwhelming amount of unwanted interest from a single person, but that the aggregated polite inquiries from dozens or hundreds of interested coworkers and colleagues could add up to something overwhelming. It's like littering.
So while being in a relationship with a co-worker may be fine, starting a relationship with a co-worker is tricky. It's like why you shouldn't hit on wait staff or flight attendants: they are there because it is there job. Your co-workers come into work every day for the same reason.
Yet this behavior is romanticised is popular culture, and has been from the dawn of time up to and including the present: Oddyseus and Helen of Troy, Shakespeare's "The taming of the shrew", tons of Fred Astaire movies, as well as modern movies like "Ghost", "Life is beautiful", "Chasing Amy", TV shows like "Sex and the city"... I could go on. Lucikly I don't need to, since TVtropes has a site dedicated to this character (the "dogged nice guy"). And note that many of these are targeted at, and very popular with, women (who are usually at the receiving end of the initially-unwarranted attention). Apparently this behaviour can walk a thin line between illegal and very very romantic.
(Oblig. http://xkcd.com/609 )
(Also "The Taming of the Shrew" is firmly in the "oh fuck no" category of 21st century society)