The histories are really a case-by-case basis, but there is close symmetry with whether you keep the name or not.
The Flames recognize their history in Atlanta, maybe not effusively since it has nothing to do with Calgary, but it is accepted, especially as time elapsed. The LA Rams have bounced around, including now 2 stints in LA, but their histories in Cleveland and St. Louis are correctly adhered. Similarly with the Browns as the Ravens are not acknowledged as the continuation (who in turn do not associate themselves with the Colts).
If you revive the team name, it’s because its history means enough, and you want to keep/revive that identity. That should remain with the city, the Jets previous history should be their own as they wish to acknowledge Winnipeg hockey. Dale Hawerchuk and Teemu Selanne did not play in Arizona, they should not be inherently associated with it. Additionally, the Oklahoma City Thunder, multiple times, have tried to get Gary Payton to be recognized and have his number retired, and he has repeatedly told them to go f*** themselves because he only wants to be associated with Seattle.