I'm definitely not for either idea (17 game regular season and/or 7 team playoff format), but I'm not sure the bolded statement is actually true. The only time 7-9 teams make the playoffs is when they win a mediocre to terrible division. As far as I can tell, the four division winners would still make it, and they'd add a 3rd wildcard, which would end having the best record possible for that slot.
Looking at recent history, the 7th spot would go to (I'm not bothering looking at tiebreakers for these):
2018: PIT at 9-6-1, MIN at 8-7-1.
2017: BAL at 9-7, DAL at 9-7.
2016: TEN at 9-7, TB at 9-7.
2015: NYJ at 10-6, Atl at 8-8.
2014: BUF at 9-7, PHI at 10-6.
Now, none of these are great teams by any stretch. Atlanta at 8-8 definitely doesn't deserve to be there IMO. But a 9-7 Giants team won the SB in 2011 (UGH) so it's hard for me to say those teams don't deserve a shot, given they'd have to win every game on the road to make it. Again, I don't like the idea, but I doubt there will ever be a year where the 3rd best non-division winner is under .500.