Yes they do, but there is more to music than chords. There are minimalist pieces that go on for hours without ever changing chords. Ravel's famous piece "Bolero" is a simple melody repeated over and over again; he uses orchestration to create the contrast.
On the other hand, plenty of composers have worked to try and expand harmony beyond its traditional boundaries. However, nontonal and microtonal music has never been particularly popular with the public. Is a piece like Penderecki's "Threnody to the Victims of Hiroshima" superior to a Mozart sonata because the harmonies are much more complex and exploratory? Most people would rather listen to the Mozart it seems.
Ultimately, Harmony is only one aspect of music. It's very important and we think about it because it is difficult to miss and lends itself well to analysis. Still, music is also affected rhythms, timbre, dynamics, phrasing, orchestration, and a number of other things, not least among them expectations of the listeners.
Complex harmony alone does not make a piece good, nor does simply harmony necessarily make it bad. The question of what makes music good or bad is huge in scope and very difficult to address. I think we should try not to worry too much about expectations of whom we should hold in high regard and simply focus on listening to the music and deciding whether we find value in it.