Just because you need one component to work doesn't mean you don't need another.
Yes, the Coyotes need a new arena in a good location and likely with other revenue streams surrounding the arena. Yes, the Coyotes need stable ownership. Yes, the Coyotes need to market properly to the individual traits of the Phoenix market. Yes, the Coyotes will need to bring in corporate support. Yes, the Coyotes will need to put a higher quality product on the ice.
The arena is just one aspect of the equation, but being set up in a stable, lucrative arena situation lets you improve the experience for fans, so when the marketing gets them in the building they're willing to come back. It lets you sell the prestige factor to interested corporate parties. And if the additional revenue streams are stable, it lets you keep quality players, which helps you put a quality product on the ice.
The arena is the foundation that lets you do everything else well.