From a purely ND perspective, I think we should be rooting very, very hard against an 8-team playoff. Staying at 4 is okay and expanding to 12 is okay. But 8 is a death knell to independence.
An 8-team playoff would almost certainly involve an auto bid for each P5 champion, one for the best G5 team, and 2 at-large bids. With just 2 at-large bids, ND would have a much, much more difficult time getting in than teams from most power conferences. If we finish the year at number 7, all it takes is any of the P5 champs not being in the top 6 to knock us out of the playoffs. Especially with how down the Pac 12 has been, that could easily happen. Being one of the two best non-conference champions is extremely difficult. It's almost as difficult as making the current playoff, except you then need to win 3 games for the national championship instead of 2 in the current system. If that happened, I really think we'd have no choice but to jump ship to the ACC in search of a more clear playoff path. God forbid we go 11-1, finish #6 in the country, and Bama, Georgia, and LSU are all in the top 5, knocking us out of the playoff. To put it another way, we'd have to watch every conference championship weekend knowing that a couple of upsets could knock us out of the playoffs because low ranked P5 champs would become bid thieves.
Under a 12-team playoff, that issue is lessened considerably. Most years, every P5 champ will be in the top 12 after the championship game. Big thieving would still be possible, but there would be 6 at-large bids up for grabs instead of 2, making life for an independent way easier.