Back when streaming meant RTP/RTSP the MPEG-4 file format, and the way bitstreams were packaged, definitely supported streaming. Not only does the format have a sample mapping table but it supports streaming hint tracks to give a server packetizing hints.
Scaling RTSP was difficult because it required two way signaling with the server and for the server to maintain client state. Using HTTP instead allowed for stateless servers in a CDN to easily scale and pushed stream negotiation onto the client. Besides simplifying the server side of streaming it made it much easier for clients switching from cellular to WiFi to maintain a stream, RTSP (and protocols like it) can't really handle clients switching addresses mid-stream.
Scaling RTSP was difficult because it required two way signaling with the server and for the server to maintain client state. Using HTTP instead allowed for stateless servers in a CDN to easily scale and pushed stream negotiation onto the client. Besides simplifying the server side of streaming it made it much easier for clients switching from cellular to WiFi to maintain a stream, RTSP (and protocols like it) can't really handle clients switching addresses mid-stream.