Think of it as - I want to fly a large airplane, but not necessarily on a schedule. Kind of like how 135 can be scheduled, 121 can be unscheduled. 121 vs 135 has more to due with payload/pax count than anything.
A lot of the cargo companies are supplemental/flag but some large aircraft pax charters are as well. Think like swift air, miami air, Omni for the pax side. IFL, Kalitta(1 and 2), the FedEx ATR certs, Atlas, ABX, ATI. All a mix of supp/flag.
If the measure of safety is merely whether people have died or not, Allegiant is on the top 5 list of safest airlines.
I think the reason they haven’t killed anyone is because of quality crews, they have literally stopped the shady MX culture from succeeding in a major accident. For anyone to allude that Delta or any other major airline for that matter, is less safe than Allegiant, is literally insane.