Teams don't fixate on toughness and intimidation like fans do. It is more about character and work ethic, on top of bringing various other valuable skills. Teams don't like guys who are floaters or don't work hard, and tough guys typically are not floaters or lazy, but they also don't like guys like what Clifford was for the Leafs: Absolutely useless and lacking skill. LA Clifford, Reaves, and to a lesser extent (and why he probably won't find anything close to a guaranteed job anymore) Matt Martin were at least able to drive possession off of a 4th line at one point of their careers and be somewhat useful outside of just hitting guys.
The Leafs therefore added guys who work hard and have some size to throw around, but also are skilled enough to be in an NHL lineup. That is why they chose Simmonds and Vesey over Clifford, and why Bogosian is on the outside looking in unless he beats out an unproven option in Lehtonen for a job (or if Dermott/Holl absolutely suck and give it to him).
If guys have character and work ethic, they will step up in the playoffs and perform when they need to. The guys the Leafs added, and currently have, are no different... And it is why the Leafs were not bullied by one of the more "physically imposing" teams in Columbus in the playoffs. If anything, we were able to do better in the tight areas than they were.