I think the Leafs need JT way more than a guy like Doughty.
The D-core certainly needs work, but it doesn't mean they need someone like Doughty. They need to add size and toughness back there. That's something they can find without spending too much money on a flashy point-producing defenseman. No more relying on Gardiner so much, get some big stay-at-home types who can long minutes. They can be pricey as well, but not nearly as pricey as a guy like Doughty.
JT, on the other hand, gives them a one-two punch at center to put the Leafs in the same category as Pit, Was, etc. It's a major upgrade over Matthews-Kadri, or Matthews-Nylander as your top two centres. IMO, it launches them into the conversation of Stanley Cup contender. Getting Doughty or Carlson instead of JT doesn't do that, IMO.
Let Shanny reel in JT, and let Dubas work his analytical magic to find a gem or two on D who is not on his last legs like Hainsey was.