My main concern with Root - and I honestly hate to be that guy because I'm still a big fan of Root - is that I don't think he wears the captaincy well. It is no reflection on your talent as a cricketer but cricket captaincy just doesn't suit some people. The fact that he has completely changed his bearing shows that it's just not a natural fit. That said I wouldn't say there was an obvious replacement without going down the same road.
The fact of the matter is a lot of people now see Stokes as our best batter not Root, and I think that shows his decline, as much as Stokes improvement.
His captaincy making his batting decline is one thing, also is he any good as an actual captain?
I believe England have 3 options to replace Root -
Stokes - this is risky, putting more burden on him, and could go the same way as Root, but i thing he would make a better captain.
Broad - vast player experience, captained the T20 side for a while as well, but if they want to keep rotating the bowlers it isn't possible.
Burns - left field choice, but don't forget he captained Surrey for a long time (and won the CC), is he going to be a permanent fixture opening though?
My choice would be Burns, yes it is a bit left field but he has the most captaincy experience which is what is needed, I think it would also give backing to 1 of the opening spots, of which I think he can be 1 definitely.
For me Stokes is far far too risky and Broad shouldn't be captain as they are obviously looking to rotate the bowlers.