The Big Ten (and Pac-12) have been proposing that should a 4-team playoff model take effect, the initial rounds would be played at the home field of the top seeds. (#4 at #1) and (#3 at #2).
It was long anticipated that the SEC would oppose this, but now they seem at least willing to listen. Part of the problem with "neutral" sites is that they are seldom neutral. Most major bowls are in the southern half of the country, which greatly favors SEC schools plus a few other southerners like Texas or California schools.
Personally, I'd love to see a team like LSU or Alabama try and play a December game in Lincoln, Madison or Ann Arbor with 2 feet of snow and a -5 degree wind chill.