Call me a cynic if you like, but the main argument against live streaming or unedited recording is that council meetings are not compelling viewing! The council of which I am a member has a local citizen who runs a community blog web site. He asked to record council meetings. He came once and made a recording, but there was some kind of technical problem. He didn't do it again.
A more serious concern is that edited "highlights" can seriously misrepresent what has happened at a meeting.
Personally, I think it's worth trying to produce a council newsletter. It doesn't have to be sophisticated, especially if resources are limited. In a small parish, it could be delivered by volunteers, in a larger parish it might be necessary to find a commercial service. Local free magazines are often willing to take on the job. Sending out news of council and other local matters a few times a year can have benefits, and also a means to promote citizen involvement.
Apart from that, grumbling about the council is probably the norm. If people aren't actually running campaigns against the council or trying to unseat councillors, there probably isn't really too much dissatisfaction. Not that I'm suggesting complacency!