No these aren't strawmen arguments, and I'm not overcomplicating this, because it really is this complex. Whether you wanna actually admit it or not, you can easily get big if not gigantic winter storms even well outside of climo favored areas without one as the Jan 2000 & Dec 2017 examples clearly show (among so many others). Is a big cold high really better for winter storms? You need 2 ingredients here and too much of one often means not enough of the other.
It depends on the setup and the kind of winter storm you wanna see, in many instances, and perhaps a majority of cases with monster cold highs you end up actually w/ too much cold air and you don't get storms at all. If you're looking for big coastal lows that provide the biggest hits to your backyard and mine, then no you probably don't want a big cold high sitting due north of NC, if you want a CAD event then obviously the answer yes. For a hybrid/overrunning the answer is more often than not yes but always or as necessary as you're making it out to be.