Correction:
1. As long as there is trickling of water through media, be it sand, coral chips, plastic balls, aerobic bacteria will use up oxygen.
2. Aerobic Bacteria will die off regardless of whether its a trickle filter, FBF, canister, sump... as long as oxygen is depleted for whatever reasons.
Bioballs, FBF, trickle filters will all produce nitrates because you can't run away from the fact they are ideal conditions for aerobic bacteria (which does the job well of converting ammonia and nitrites to NITRATES). Fouling due to entrapment of bio-matter will happen to a different extend with each method but much lesser with the FBF.
Most systems can cope with ammonia and nitrites once the bacteria is established when the cycling period is over. It's the problem of having a tank that processes nitrates naturally instead of troublesome water changes, setting up a hard to tune denitrator, using expensive enzymes such as AZNO3 etc... and that's where NNR comes in, eg. the use of DSB or ample LR.