Well, indirectly, if you have bioballs and use them as most do, as both a mechanical and a biological filter, yes the bioballs contribute to nitrates, because, as you said, debris get caught up in them, resulting in insufficient breakdown of nutrients. The end result is nitrates. The same can be said of ANY media, including carbon, ceramic pieces, filter pads, etc. All of these things provide surface area for the bacteria we need to run our tanks; however, unfortunately, they also clog up quickly and, to avoid their mechanical filtration, the hobbyist must change or clean media/balls very frequently. And, ironically, cleaning these things destroys their biofilter capacity.
This is way too much trouble for most set ups, when you can set up a tank that will perform so much of the filtration for you. Who prefers biofilters, wet-drys, and canister filters to a natural set up with a DSB, live rock, refuguium? At the end of the day, a natural system is much more pleasing, its more in keeping with what we try to achieve for our tanks, and its not cumbersome. Natural filters are actually fun to develop, as opposed to being a weekend chore that we need to set aside time for maintenance.
Who enjoys showing off their bioballs and filter pads, as opposed to those who can be proud of a thriving DSB, macro tank, refuguium?