Throwing all the colors from every alternate jersey worn over the last decade onto a square and then saying "See! We lack a cohesive color scheme" simply isn't representative of reality. It also doesn't follow that the answer for too many colors is the introduction of yet another (black) as the primary color - especially when others (the green, purple and yellow Mardi Gras colors) have much more of a connection to the team's name and history.
The 11-color gradient on the left comes from the "City Edition" jerseys that Nike makes for Utah. They're cool, but they're an alternate that has nothing to do with the team's primary color scheme and everything to do with Nike stretching to come up with a tie-in to the locale. Jettison those colors if you really want - they were alternates anyway.
The colors on the right come from the late Stockton-era re-brand. Again, they make for interesting alternates, but I don't think anyone considers them anything more than alternates from the era of Utah's fall from grace. They're cool only because they are so ugly. No one would cry a single tear if the Jazz moved off those colors as well.
That leaves us with yellow, a couple shades of green, a couple shades of purple, and a couple shades of blue (and I'm being generous by lumping in the blues from the D-Will era re-brand). Consolidate those colors if you want - that's fine and no one would say boo if we only used one tone of purple or green or blue moving forward.
The answer for all this is not to go, as the uniform community says, "Black for Black's Sake" (or BFBS); it's to identify and push a cohesive set of colors that connect with the team's heritage and tradition.