Already half the league makes the playoffs. In this scenario it does adequately reward those teams that work hard through out the season and are rightfully better. With so many rounds in the playoffs anything can happen and basically creates a second season as opposed to a playoff between the best of the best.
I do not think that the NFL should expand the amount of teams that make the playoffs. They already have the perfect playoff system and I would be upset if they changed it. You cannot just let any and everyone into the playoffs. It takes away the allure of making it there.
The playoff brackets in the NHL are already enormous. Frankly there aren't many recent examples of "NHL" and "expand" being in the same thought that were good ones, this would be no different. The Stanley Cup playoff are already an insane grind, players don't need additional rounds and neither do the fans.
There are arguably already too many teams involved in the playoffs. Expanding the playoffs is not necessary and will only drag the season out longer than it should be. They players will be more tired and the eventual Stanley Cup games will probably be of poorer quality due to fatigue. It is just a money making idea by the owners and the league.