The only way that happens is if they give Hayward the five year max like Paul George got, and that just is t happening. The reason they won't lose other players is because burks and kanter are not max guys, and burke's rookie deal will not end until Hayward's extension is done, assuming he gets the four year extension. The only thing it really affects is the ability to sign a max free agent, and that was never really a concern here anyways, as it's not happening.
Another consideration is that the salary cap is going to be a lot higher at the end of Hayward's contract than it is now, so we will have more ability to sign other players/extend the ones we have.
The real problem with keeping the team together comes after Hayward and favors deals expire. If they are both max players at that point, you want to keep them, but we might have Burke and hopefully Jabari/wiggins playing at a max level too. So at that point, you have to trade or not re-sign someone. But that is 4 1/2 years from now, and not hinged at all on the contract extension that Hayward signs at the end of this year.
While you make some fine points aren't you also making a few assumptions. Right now Burks and Kanter aren't near MAX guys but they still have another year before their contracts are up (I believe). Burks has been playing very well since Hayward got injured and Kanter just had a monster game against Detroit. Now consistency is still both an issue with these guys but if you end up giving Hayward the Max then you end up setting a bench mark for all the other players. If Burks out performs Hayward then you a problem on your hand. I agree that the Jazz will definitely have issues once the contracts of Trey, + our lottery pick 2014.
I am not very familiar with the CBA but I thought the salary cap was decreasing with this new deal or was that the percentage of revenue sharing. Besides a team is less likely to want to pay the luxury tax since the penalties are greater. You're still going to need to fill out the rest of the roster with players other players. The Core5 + top 5 pick + another first round pick. Is the rest of the roster going to be DL or cheap vets like John Lucas.