By extracting only lines containing "mms" you're losing all the "on-air" channels, "in diretta" (rai1, rai2, rai3, rai news 24, rai sport +, rai storia, rai edu 1), and a lot of on-demand programs including parts of the Sanremo Festival ( sorry ), documentaries and so on.
The majority of streams are encoded in the form of "http://mediapolis.rai.it/relinker/relinkerServlet.htm?cont=<put here a number>", which in turn links to a mms: stream.
The mms relinked streams urls are changing really fast, so it's no use caching them for more than 10-20 seconds.
Try the shell script and you'll see.