Byes I do think are an important consideration, but let's put that aside for now.
This week and conference championship week would be the key weeks for games mattering in the old system and not mattering now. This year, Ohio State/Michigan, Indiana/Purdue, and Ole Miss/Mississippi State are games that didn't matter for either team other than seeding.
Oklahoma/LSU, Notre Dame/Stanford, Alabama/Auburn, BYU/USF, Miami/Pitt, Virginia, SMU, Tulane, James Madison, even the Duke game all matter because of the new system when they wouldn't have in the old system.
So even in this week, more games matter by a good margin. And if you back up three weeks to a month, there are 0 games that didn't matter whatsoever (because even an undefeated team could lose 2-3 games straight and lose their spot) and way more teams that were alive if they could win out.