I think you've got it slightly the wrong way round. We don't do this, instead the DM latches onto their target man, allowing both CBs to drop deep to mop up or track runners.
That was the big lesson from the Everton 4-0. Before then we did it as you said, 1 CB would engage, the other would drop off, but after that massacre where they'd have Davies, Barkley and Lookman running after Lukaku's flick ons against just 1 CB, Pep changed it so Fern would compete for long balls and allow both CBs to drop off.