The Jazz aren't a team full of crappy dumb players:
Trey and Gordo are plenty smart, but are lacking physically (I know many disagree with this physical assessment).
Alec and Favors are more gifted physically, albeit not quite elite (at least as far as Alec's strength is concerned). They also seem to have an adequate feel for the game overall.
Kanter seems lost out there a lot of the time.
Those Deron-Boozer teams were incredibly intelligent. Despite the success of smart teams, intelligence still seems to be undervalued by GMs, which partly explains how San Antonio is able to assemble amazing, deep teams without going into the LT. With that said, as opposed to a lot of individual skills (especially rebounding and on-ball scoring), which seem to display diminishing returns, there seem to be increasing returns to passing and overall team play. That is, if you have a team with very little talent or smarts, finding a player who does something well individually (eg. Al and on-ball scoring) will have a greater impact than adding a smart player. Smarts become increasingly valuable as you have more smarts. Having the patience to build a team correctly can be difficult, as shiny, young players with flashy individual skills put more people in seats in the short-run.