When listeners can choose specific songs, that's called "on-demand" listening. That includes being able to rewind or replay a song which has just played. On-demand listening is a category of streaming music which requires significantly higher royalty payments to copyright holders and record companies.
Currently, every Internet radio station in the U.S. must abide by guidelines set forth in a federal law called the Digital Millennium Copyright Act (DMCA), which places certain restrictions on what we can offer our listeners. (If you're interested, you can view the text of the DMCA in PDF format here. The section that regulates Internet Radio is listed under Title IV, Sec. 405, "Scope Of Exclusive Rights In Sound Recordings; Ephemeral Recordings" on page 33 of the file.)
The webcasting license we operate under only allows "limited personalization" of our channels. This is why we only allow listeners to deselect (in other words, ban) a limited number of artists and songs they don't want to hear, rather than allowing listeners to pick specific artists or specific songs they do want to hear.
As far as copyright holders are concerned, allowing listeners to choose the specific songs they want to hear when they want to hear them might discourage those listeners from buying CDs or digital downloads.
Hopefully we've found a solution that everyone will be reasonably happy with.