But some conferences do the NFL before and after kickoff BS while some don’t. And it’s not always with a change of possession as it seems to depend on how recently there was the last break.
That's not a conference thing.
There are a designated number of media timeouts per quarter, based on the network. Most of the time, it's 3 in the odd quarters and 4 in the even quarters.
If you have a team taking 7:00 or 8:00 for a scoring drive, that jams up the breaks.
Example:
Start of period - 3 and out
13:00 - they're not taking a break after one short possession
10:00 - Team A FG (break #1)
3:30 - Long TD drive by Team B (break #2)
At this point, the producer knows they still contractually have to get either 1 or 2 more breaks in
yet this quarter. That results in the break after kickoff (break #3).
If it's a 4-break quarter, now the truck is praying for another quick possession (3 and out, ideally) or some other stoppage in order to get that last one in.