think having him on the pitch gets the best out of Bobby too as it allows Bobby to press higher up the pitch
Actually, thinking about it, players who allow other players to play higher up the pitch are some of the very best players to have, and it starts in goal.
Alisson pushes a defensive line 5-10 yards higher because he's so good off his line.
VVD and Gomez add another 5-10 because their recovery pace is so damn good and they're so comfortable in possession.
Robertson and Trent Keep that solid, and keep teams hemmed in because they can act as auxiliary wingers while still maintaining that defensive line.
Fabinho, again, a player that physically dominates his zone but has the technical skills to get it to players in their zones. He's the one who allows the 8s to focus on creating attacking opportunities.
And then the 8s themselves - and what a difference it makes when it's them circulating the ball to the front 3 who are all occupying the opposition back 4, rather than having to either drop deep all the time to get the ball, or move ahead of play all the time to create a threat.
And the difference it makes when Bobby is harrassing their CBs rather than their DM - you're right that it's no coincidence that Firmino's own performance was off-the-charts good against Burnley. I mean he was fucking magnificent, just a relentless engine of threat creation.