It seems to me the Jazz were in a hurry to rebuild after Stockalone. They maxed AK in a heartbeat, then rushed to bring in the only two FAs they could get, two PFs who, as it turned out, weren't that good together.
In other words, the rebuilding plan wasn't much of a plan. Players were slapped together reactively whether they fit the system or not. Brewer was never going to be the ideal SG. Neither was Almond. Koufos wasn't the full-time powerful pivot we wanted. Neither was Fess. The Jazz FO was a bit passive and waited years to see if things would magically "work out." And they didn't. Maybe there weren't good opportunities to build the team better. Drafting late in the 1st round may have been hopeless. So they got stuck as a top 6 - 8 team in the league unable to get past the 2nd round.
The good news now is that the Jazz have a player in Favors that they should be able to build around. He should become the most reliable big man of the last two drafts. The Jazz also have a good number of decent role players who have potential to get better. Now they need an elite guard.
I don't think they just threw people together. The inside defensive combo of Boozer and Okur was bad, but other than that everyone seemed to complement each other pretty good. At the time, that team was actually a pretty solid team (Williams, Giricek, Kirilenko, Boozer and Okur -- though admittedly Giricek didn't play much when Williams emerged but you get the idea [sub in Korver]). The problems ended up being injury (obviously) and chemistry. It was apparent after the first time we got wiped out by LA that we needed to lose Boozer. Though we were injured, that was never an excuse to just "wait until we get healthy". It took two more years of the same team and two more years of getting wiped out by LA before we did anything (and that was only because it was a passive decision) and let Boozer walk. While I agree that something needed to be done sooner, I can't really complain about the assembly of that team because that truly was a talented team, despite seeing where it ended up taking us in hindsight.