You could, but there are ways of breaking boom chains, etc.
It’s true that having built something generally helps, but you also have to consider that in medieval politics, proximity is hugely important. White Harbor being right next to Moat Cailin would give it more day-to-day influence than Winterfell, which is 400+ miles away.
Whereas having the Canal pass by less than 50 miles away from Winterfell (and through territory that Winterfell itself owns) gives me a lot more practical control as opposed to de jure control.