What you have to keep in mind here is that the FAA feels (correctly, in my opinion) that a transport category airplane neither knows nor cares what sort of operation it's involved in (private, charter or airline). It's always going to be big, heavy and capable of a lot of damage. So, the regs essentially require all such aircraft to be operated more or less the same way. Thus, for private operators we have Part 125, while for charters we have 121 Supplemental status, which essentially establishes any charter operator that flies airliners to, in fact, be an airline minus a regular schedule.