Alright, so I actually think I figured out what happened here. It is of course context-dependent, but I would argue it is especially context-dependent:
I. The Jazz are operating under this basic framework ("The Plan"):
-A. The want to spend as little actual cash as possible during this era.
-B. So they are trying to get as close to 90% of the cap as possible (for those that don't know, teams are required to pay a minimum of 90% of the cap on player salaries. This means teams are throwing away utility if they have cap commitments below that figure or spending cash if they are above it).
-C. Danny Ainge has incredible power, only technically less powerful than Smith but in reality almost equally powerful (he is the alternate governor, after all)
II. As it stood and basically continues to stand:
-A. If all players on the Jazz with player options opt-in for '23-'24, they are at ~$105 million. This is important for calculation since the Jazz don't control if the players opt in or out, so to be conservative, they plan on them opting in.
-B. If the Jazz exercise the team option to keep Beasley next year, they are damn close to that 90% of the cap (~$121 million)
III. So, the operating parameters on a Bogey deal were:
-A. Maintain at least the option to get close to the 90% of the cap figure or below for next year
-B. Acquire some kind of utility; draft assets ideally, at least if deemed of sufficient quality while considering criterion A.
Reports indicate that in the prospective Phoenix or Miami deals, the Jazz would've had to take on longterm salary to get the draft assets, which violates one of the operating parameters. We're not ownership, and that's their prerogative. Fine. What about the Lakers deal? We'll come back to that.
The overarching operating framework (section I.) then kicks in, whereby they try to satisfy all criteria as much as possible (save CASH, maintain or enhance flexibility, satisfy Ainge). So they find the Detroit deal which does so (saves cash, gives a mostly-unguaranteed team option which you can argue could provide at least increased optionality, and Ainge gets one of his guys).
So now we come to the Lakers. Contrary to a lot of the narrative about him that reigns after he makes a great deal, I think there is a lot of evidence that his pride is often misconstrued as patience, and that that takes the lead in decision-making. Reports indicate that the Jazz basically could (/should) have satisfied ALL criteria above (I - III) by consolidating players and gotten ONE probably-unprotected 1st round pick later in the decade. But Ainge demanded TWO! And the first rule when working with Danny Ainge is when he sets a price, he only minimally budges. There are no more deals to make after that one, so the argument that he has to maintain negotiating integrity for the next deal is pretty hollow reasoning. Maybe the Lakers make the same calculation about JC that is premised above, so they want the Jazz to take back greater salary in the deal which has big cash ramifications this year (maybe not, though). So Danny's pride probably ruled the day because he didn't think he was getting enough back, went and found a pet that saved Ryan cash, and they moved on.
Where this gets frustrating to me is that without taking THT, there are fewer constraints on salaries that go beyond this year, and there's the possibility that JC would've been included in the deal to the Lakers, too. And Vanderbilt. But Ainge has a boner for THT, Vanderbilt, and Olynyk, so they stay.
Summary: Jazz should've taken the Lakers deal but didn't either because of cash implications this year, Danny's pride, or both; and the Jazz are planning on keeping Beasley (but are equally happy that he has a team option).