Rodgers also didn't have the confidence to work with the system. I don't know if that's age or his personality. But with Klopp we're seeing a manager who trusts others to do their job. Also suspect Peter Moore is a key appointment -- the set-up is reminding far more of 'back in the day' despite the new technical roles; there's a quiet efficiency to it. No more photos with Fowler.
Rodgers didn't even try to work within this actual system mind, hence the clusterf*ck that was the transfer comittee. Hindsight is a wonderful thing, but the club likely should have had the structure set before emplying a new manager, and given an ultimatum as to how to work, rather than him saying 'nope won't work with a sporting director'. But anyway, thats been talked over and over of course.
And this is how Kloppo has always worked to great effect, so is very comfortable doing so, he's worked so well in the past with Heidel at Mainz and Zorc at Dortmund, and now it seems Edwards too. And it's a normal way to work for coaches in other leagues.
I suspect more and more British managers will have to get used to this way of work, as more clubs over in the UK seem to be now using this structure.