The announcers don't usually announce the Friday sessions, they are presented as a highlight package on the Saturday Qualifying TV show. So they are doing extra work with the talent and production teams (on screen graphics, replays, etc). Then there is the issue of infrastructure on ESPN's website and the bandwidth requirements of the users streaming the show, not to mention the bandwidth requirements on site at the track to upload it to ESPN so we can stream it. If this is done via their satellite uplink (the way TV is done) rather than some sort of land based connection, the costs can be quite prohibitive, not to mention that locks out a channel on the satellite that can be used for no other purposes during that time.
So it makes sense to keep the Sunday feed up all day on ESPN3 if they are using satellite links back to ESPN, because you would not want to bring the link up and down after every session and risk not getting it back -or- losing your "spot" on the satellite. At least we still get to watch alcohol and pro mods on Sunday!