re: How does it happen that Bama plays so many more teams with a bye than anyone...

The SEC makes out the schedule for each of the SEC schools. Since they want SEC games every week they schedule teams without games against SEC opponents throughout the season, and it means some teams will have byes since the season is 13 weeks long and teams only play 12 games. Other schools who can elect to use a bye week to prepare for Alabama. It is a sign of respect for Alabama that teams would like two weeks to prepare to play against them.

The SEC office isn't doing it to punish Alabama. It is just a consequence of the SEC trying to maximize revenue by making sure there are SEC games every week of the season.