Carolina played great football while Atlanta and the Saints did not. Carolina rose above the rest of their division and won in the home stretch when it mattered most and that's why they rightfully got in the playoffs. The niners didn't.
The reason division games are so intense and the rivalries are so fierce is because of the current playoff format. Every division game matters. You change the playoff format then there is no reason to play each team in the division twice a year, the games are less important and that means those great rivalries across the NFL wouldn't have the same intensity.
By having the division winner make the playoffs is the reason division games are so awesome.
It's not a good enough reason to change the entire format just because once in a blue moon a team with a losing record makes the playoffs. It's very rare.
More often than not, a team with a sorry record makes the playoffs because their division sucked that year. It happens often. The Giants are the only case I can think of that did well in the playoffs that had a sorry record.
Games would still matter the same, and schedules would still hold the same matter of importance, if not more. You deal with long stretches of the Patriots beating up on the Bills, Jets and Dolphins, the Broncos beating up on the Raiders, etc... with the current format. And those teams get to play sorry teams twice per year because they are in the same division.
It'll still make some of those teams to play each other every season based on geographic proximity to each other, and for the sake of their history playing each other. But the league wouldn't suffer any IMO.
If it happens, cool. If it doesn't? Cool. Not a big deal other way but I think it would put teams that are more deserving.