Neutral sites are very expensive to attend for the local fans (travel, lodging, time-off work, booze, etc). It's somewhat justifiable when it's a once in a lifetime scenario (ie Indiana this year). My UGA friends went to everything the first year not so much the second year. At 16 teams, there is a high probability that half the teams in the playoffs will make it every year. At some point those people will stop going to the games.
You could give the higher seed the home field advantage in the first round. In the second round, put the remaining 8 teams in a hat and draw for home field. Do neutral sites for the semis and finals.