First, I can't comprehend thinking that jazz sounds garish and cheesy... like... at all. I mean, the common negative reputation would be for it to be considered pretentious and stand-off-ish, which is the polar opposite of that. Unless you're talking about smooth jazz or something, then I can see it.
Showy, I can possibly see with the more normal styles of jazz, but free jazz? No ****ing way. Free jazz can be criticized for being narcissistic, alienating, and self-indulgent, but nobody plays free jazz to show off their bravado and technique or to put up a front for an audience-- it's closer to communicating a mentality of "**** what everyone else thinks, I'm letting loose, becoming unhinged, and letting my raw, expressive instincts guide me."
In that sense, I would associate free jazz to being the punk music of regular jazz..... It's raw, uncontrolled, and irreverent, which would be completely anti-thetical to being showy and melodramatic.
While I love Jazz Fusion, I think you can far more reasonably make a case for Jazz Fusion being overly showy and grand-standing.