What's bizarre about the bye weeks in the current scheme is that there are a few weeks in the middle when no teams have the week off.
In the 2023 season, four teams have byes in week 5 (go 'Hawks!), two in week 6, six in week 7, NONE IN WEEK 8, four in week 9, four in week 10, four in week 11, NONE IN WEEK 12, six in week 13, and two in week 14. That just strikes me as silly, and as an obvious additional way for the schedule makers to put their thumbs on the scale.
I think they oughta do something like having just three or four possible bye weeks clustered in the middle of the season. If it were three, I'd make them weeks 8, 9, and 10. If it were four, I'd make them weeks 8, 9, 10, and 11, so that to the extent it's skewed, it's skewed toward giving players a little more rest later in the season rather than earlier. They could also have different numbers of teams on byes in different weeks (that's how it is now) to balance that skew.
When the schedule expands to 18 games, the calendar will wreck what would probably be a good solution. If each team had two bye weeks in an 18-game season, it would be less difficult to distribute byes fairly. The problem with that is that they've already reduced the preseason to the point that people are wondering if teams aren't fully ready at the start of the regular season, and the Super Bowl is already pushing into the middle of February, so adding two more weeks to the regular season looks infeasible. Just adding the one for the 18th regular-season game will be hard, and because they're not going to want to add another bye week, I suspect there'll be more injuries.
Week 12 starts on Thanksgiving, so that might be a big week for people watching NFL games, but in both of the fairer bye-week schemes I suggested, every team has already had its bye by week 12. However, at least I can understand that there may be some business reason for having no byes that week. I really don't get having no byes in week 8, which ends just before Halloween (MNF is on the 30th).