I think what he brings a lot to the team is that he provokes the most fauls, so many that if we weren't Barcelona our opponents would get sent off in the first half. But thats the problem, only after 30+ min referees even consider pulling out their yellows, and they consider its Neymar so even if its a yellow worthy challenge you already know referee won't pull out his cards. I believe with video refs next season this might change and Neymar will be even more crucial for our team.
About that part with fouls, often it seems as if he is "enjoying" in those fouls.
You probably know that situation when he gets the ball, hog the ball and starts to dribble towards our goal (with the defender on his back all the time) and then in one moment he stops, holds the ball again, turns his back/ass towards the opponent and waits until the opponent fouls him (kicks his legs).
If the opponent doesn't foul him, he waits even longer and longer until an opponent finally kicks his legs.
Then he falls on the ground, holds his legs and looks at a referee more or less saying: ref, did you see? He kicked me.
More or less, I see those actions of his as: I will take the ball and I won't pass the ball to anyone until an opponent will kick me.
To some extent, as if he is provoking fouls and as if he isn't interested in passing the ball to someone else.
He just waits (this is my view) for a foul, even though he can stop that duel easily with passing the ball to Busi/Iniesta/Alba/Umtiti.
Another interesting fact: in a match against Real, when there was NO Neymar on a field and when he wasn't hogging the ball and provoking fouls (my view, again), RM made only 2-3 fouls in the first half (Casemiro on Messi and Marcelo on Messi).
Again, this is only my view, but if Neymar was on a field, RM would probably have 10 fouls in the first half, with at least 5-6-7 fouls on Neymar.
Again, this is just a personal view on this "problem", but I really see those Ney's runs (which end as fouls) as:
1) a normal player will take the ball and pass it eventually, and he will get fouled once in 10 actions
2) Neymar will take the ball and force actions/dribbles/duels which often have 0% chance to create anything (since he is dribbling backwards at the centre of a pitch) and he will hog the ball until he gets fouled and that will happen in roughly 50% in those actions.
I will draw an analogy with Pep's Tiki-Taka:
= since you are not allowed to take risks and lose the possession (when trying a counter), you will more or less "force" the opponents to sit back, and return to their defensive shape, and park the bus since you are giving them time to park the bus each time because you don't want to play a faster action
So, it isn't as if opponents are parking the bus ONLY on purpose against Tiki-Taka, but more or less, teams who play Tiki-Taka are "forcing" the opponents to park a bus.
On the other hand, if Barca will play more risky, with more counters, an opponent won't be able to park the bus that fast.
So, to some extent=HOW you play is reflected in the response from the opponent's team.
The same is (imo) with Neymar and fouls.
Without him on a field, our players don't hog the ball and nobody is "looking" to get fouled on purpose.
And opponents will have less fouls on our players.
When Ney is on a field, his style of play (but I am not talking about dribbles here, since Messi also dribbles but gets fouled way less than Ney, since he isn't "looking/provoking" to get fouled on purpose) will just call or force the opponents to foul him when he does his backward-dribbling-hogging-the ball-run.
And then, when Neymar does that backwards dribbling a few times, he will already start fights with the opponents who kicked his legs, and then in upcoming minutes, the opponents will start to hit him even more and more even in regular actions (when he is dribbling TOWARDS the opponent's goal).
So, in the beginning, Ney is fouled in a silly way, because he is hogging the ball and asking for a foul.
Then he gets pissed off and probably says something to opponents.
Then they get pissed off and after that, every action is a horror show with criminal tackles.
All in all, one more time, without Neymar on a field, RM almost didn't create any fouls on our guys.
That's not a coincidence.
So, about that part how Neymar is fouled a lot, a huge part of guilt is on him, how he provokes the opponents early in the match and then later it all ends wrong both ways.