Doesn't really make sense.
Whenever you change a manager it brings a change of style.
Moyes to Martinez is just as big a change as Martinez to Allardyce. In fact probably bigger when you consider the transition via Koeman.
If you're changing manager it's often an admission things haven't gone well. So the last thing you try and do is replicate the precious managers style.
Of course every manager is different and will apply different tactics relative to the previous manager, but some only need to tweak a few things within an existing football framework whilst some demand a complete overhaul.
The benefit of the former scenario is you should have most of the players to implement the new manager's slightly revised system and might only need 2-3 players in the next transfer window to improve general play. The scouting team at the club might have already found the right targets to fit into the new manager's system.
The problem with the latter scenario where the new manager demands a complete overhaul of the football philosophy at the club is they have to work with the existing players at their disposal who could very well be ill suited to implement their vision and when it comes to transfer window time, that manager will want to bring several of their own kind of players which could risk upsetting further team spirit.
Martinez actually did well at the beginning of his time at Everton because he practically improved on the solid if unspectacular formula that David Moyes had left behind but I feel his biggest error was deviating too much away by the end of the first season, we'd been known before for being strong defensively but by the last 2 seasons of the Martinez era we were every opposition striker's dream to play against especially on the counter attack and set pieces.
Everton used to talk about the "School of Science". What on earth is that supposed to be and why hasn't that been used as a framework to direct our football and staff recruitment?