It seems to me that what BBZ is envisioning is Luis Enrique 14/15 style football. It's possible with the new additions in attack (Dembele and Malcom, also Coutinho) - but I don't believe Valverde sees things the same way. As many others have mentioned: he is a "play it safe" manager.
In the end it's always down to the coach to make such a change from possesion-prioritizing football to a style that bypasses the midfield more quickly. A coach can instruct the defence and his midfielders to play more lateral passes and to focus on reaching the opposition goal area as quickly as possible, in other words: to move the ball forward quicker and thus take more risks. Class players will be able to adapt to such instructions (see Xavi in 14/15 compared to 13/14; played way more direct, forward passes, long balls).
I don't see it happening with Valverde though. The main reason - besides Valverde's probable unwilingness to play such a style of football - is Messi. He is now even more of a playmaker than he was in 14/15 (I would argue, last season, he was our only one). With him in the middle, the orchestrating of attacks will always be based on him picking up static balls from deep, trying to move the ball past a midfield line with one-twos or dribbling multiple players plus the occasional long ball to Alba.
The two options that remain are: put Messi at RW (good luck, he won't stick to that position, won't defend, also: what do with Dembele/Malcom in that case?) or have him play as a false 9/deep-lying forward in which case he would have to stay closer to goal at most times and let other players do the creating. The latter is a scenario I would like to see happen regardless of how we end up playing. His goal in the WC against Nigeria comes to mind. If Banega can function as a playmaker/chance-creator for Messi, I don't see how Coutinho f.e. can't occupy that role for Barcelona.
Since most of this is now kind of off topic, a few words on Arthur's role: I think that his biggest feat is that he adds safety and security as well as sturdiness to our midfield. As many have pointed out, having him on the feild seems to have given players like Roberto and Rafinha the confidence to take more risks on the ball and move more freely (might also be due to the fact that it's preseason and some players seem to really shine only when there's no pressure, like Denis in the preseason of 2016/17).
Now some have said that he should be doing more chance-creating and that there are many other CMs that can shield a ball, keep possession and who are good in link-up play. However, in many (big) games in the last 2-3 seasons we've been exposed as not that press-resistant. Whenever a team attacks our backline and midfield directly (Chelsea at Stamford Bridge, Roma 2nd leg) I often found myself incredibly nervous when we were on the ball in our own half with guys like Rakitic, Paulinho, old Iniesta and off-form Busquets (don't make me mention Gomes, Denis) trying to sheild the ball. I hope my pulse will be a bit lower in those situations with Arhtur in the mix of our midfield and I'm catiously optimistic about his other qualities too, excited to see what he'll bring to the table once he fully integrates into the team and develops over the next seasons.