Its sounds all logical. But new management doesn't always think in those terms. It's all about making a splash.
They will need a new CEO to look after and manage their investment, understandably so. Arnold/Murtough are all part of the previous regime, tainted some might say. And indirectly ETH (a hire of the previous fecked up ownership) or at worse they just drip dry him and not support him like what happened to Tuchel.
It wont be unsurprising if this happens. Seen it enough in the corporate world whenever you have a new CEO come in, he brings in his own team -- with even 180 degree change in direction.
Circumstances are pretty different.
ETH:
-> wants to have holistic control of the team, not just restricted to tactics
-> his signings are all spot on with every one making it to first team (except maybe Dubravka who was a backup anyway)
-> has improved the culture tremendously by bringing in players with the right mentality and getting rid of troublesome ones (Ronaldo, Bailly, Telles - you could argue Henderson, Lingard, Pogba, Cavani were on their way out anyway)
-> clearly knows where he wants the team to be in the medium to long term
-> has shown clear indications of promoting academy players
Tuchel, on the other hand:
-> was lost beyond a tactical role
-> rode on the performance of previous signings
-> brought in Lukaku, Fofana, Koulibaly, Aubameyang, Sterling, Cucurella (some may eventually be good players, but wouldn't want any of these near our first team)
-> sold pretty much all their youth players who showed some promise
-> focused on short term results and ended up with a squad leaving a lost culture
It'll just be a case that the new owners see where ETH wants to be, and will back him. It'd be stupid not to do so, given his track record with Ajax and current progress with the squad.