goon I don't think it's staged to be fair, the two of them are just argumentative by nature. You could see Carragher starting to lose his cool on the Everton segment. The two of them care too much about being seen as knowledgeable to come out with click bait material.
It's not staged to the extent that they're reading a script but, as with almost all 'celebrities', they're effectively playing a character that hopefully attracts eyeballs. Fortunately for Neville, he's been training to be an unlikeable cunt all his life.
I agree on Carragher being a better pundit - put him next to Henry and Micah Richards on the Champions League show that he does and he comes across as much more relaxed and more interested in being entertaining than knowledgeable. I'd much rather have ex-footballers share their own personal anecdotes and experiences rather than make predictions.