You are getting something wrong… RTSP is a realtime streaming protocol. Meaning, you can stream whatever you want in real time. So you can use it to stream LIVE content (no matter what it is, video, audio, text, presentation…). RTP is a transport protocol which is used to transport media data which is negotiated over RTSP.
You use RTSP to control media transmission over RTP. You use it to setup, play, pause, teardown the stream…
So, if you want your server to just start streaming when the URL is requested, you can implement some sort of RTP-only server. But if you want more control and if you are streaming live video, you must use RTSP, because it transmits SDP and other important decoding data.
Read the documents I linked here, they are a good starting point.