There hasn’t been a single safety issue identified with Part 380 carriers complying with the rules applicable to Part 121 operations. In fact, the rulemaking even notes that “the FAA has adjusted its oversight of these increased operations” and has not expressed a concern about JSX or similar carriers.
The only reason the agency cites for potentially banning their operation is they’ve grown, but that is literally what the rules – and the Department of Transportation – are designed for.