He shouldn’t. Matthews hasn’t won any major awards yet and really, there aren’t many comparables he could use to extort the Leafs with to get to $13m+. The only way he gets more than McDavid is if a team like the Coyotes offer sheeted him and even then, that’s a big IF.
Matthews would essentially be leaving a deep team with serious Stanley Cup aspirations to be a franchise player who has to carry a team on his back with all the pressure squarely on himself while hoping to maybe make the playoffs. If I was in his position, I’m not sure I’d make that move.