Utah is a small market team that could struggle to add big names in free agency (granted, winning overrides everything) and they might not be able to afford three big time contracts (Hayward, Favors, Gobert) not to mention they will probably want to hold on to other players (Exum, Hood).
They already have Lyles, who could replace Favors and is on a rookie contract. They could add another cost controlled player on a rookie deal with the third pick (a guy like Hield would be great for them) and a future pick or one of our young guys. By not picking up Amir's option they could save some money and try to retain the talent they already have.
I am trying (unsuccessfully) to find an article from this past season that talked about the Jazz and why moving one of their players would be a great move. The main point in the article was that if they tried to resign Hayward, Gobert, and Favors when their contracts were up they would be using the majority of their cap space on those three guys. Trading Favors while they have a solid backup plan in Lyles might be a good move for the team for both the short and long term.