I think the thing with Mott is that he is quite a diffident character, as is Buttler as a captain. Mott with Morgan (which is what was expected when he was appointed) would work fine because Morgan was very definite about what he wanted, but there does not appear to be the chemistry between the two at the top.
Buttler has to stay on for the time being - aside from the fact that, as awful as he has been (and he narrowly pips Livingstone and Curran to the title of worst England player at this World Cup), it is one tournament in a glittering ten year white ball career, there are not really any other options. Stokes, Root, Bairstow and Woakes will be made to prioritise other formats, Ali and Willey are gone and Malan seems to be the scapegoat. The rebuild should focus on getting a "Buttler" team - and focus on younger talent.