If you're going to expand the field (which I don't agree with, not that that counts for anything), I think 12 is the perfect number. You can give automatic entries to all of the Power 5 conference champions, the top 1-2 Group of 5 teams, and fill the rest with at-large bids. You achieve multiple objectives, including giving the small guys a foot in the door, rewarding conference championships, and, in most cases, teams aren't going to play more than 3 postseason games, alleviating concerns of those who actually still think academics are important and want to minimize disruptions to the academic calendar.
If you limit it to 8, in most years you won't be able to accommodate all 3 sectors (P5 conference champs, G5 top 2 teams, and at-large bids), unless the P5 conference champs all happen to be in the top half-dozen or so teams, which is very unlikely. If you expand it to 16, the teams who make it to the championship game will have had to play 4 postseason games, which is too many; plus, the #1 seed has no advantage in the bracket over the #16 team. As you stated, getting a top 4 seed and a bye is a huge advantage, which they deserve and should get as a reward for an outstanding regular season.