Actually fining is more likely to have an impact on flavor and aroma than filtering. The fining agents will bind charged particles and may just as easily bind some flavor elements with charges, even if they are very small particles. A filter can remove particles with charges, or it can be neutral and only retain particles based on size. If using a neutral filter, the elements that create flavor and aroma are very tiny and you'd need ultrafiltration (below 0.1 micron) to remove them. The typical sterile filtration with a 0.45 micron absolute filter (or 0.2 micron) simply won't filter out those particles - they pass through.
Filters can affect the flavor, especially if they are not flushed and rinsed properly, and if the wine get excessive oxygen exposure during the process. This oxidation probably accounts for many of the anecdotal reports where people describe filtering as having altered the flavor. In a variety of scientific studies, when done properly, filtering has been shown not to harm wines. Emile Peynaud actually went as far as saying that filtering would invariably improve the outcomes. Now my palate is not sensitive enough to pick up on those subtle changes, so I have to defer to the scientific experts with the trained tasting panels that have studied these issues.
Still, the fact is yeast taste bad. Don't believe me? Well taste a heaping tablespoon or two of your wine yeast (before or after rehydration). Ghacck!

A yeasty, cloudy mead usually tastes crappy. Filtration can eliminate those bitter little buggers leaving the wine tasting cleaner and fresher.
In my experience, filtration does not cause a loss of flavor or aroma, and I have definitely stripped some using Bentonite and fining agents so filtration can be a useful and practical technique.
Medsen
EDIT - On another site I saw Tim Vandergrift referring to an interview from some years ago with Christian Moiuex, the owner of Chateau Petrus (yes, that Petrus - the super expensive Pommerol) who replied when asked why he used very tight filtration on his wines, "Because I don't hate my customers. Only a fool thinks unfiltered wine is superior." I'd love to track down that interview to read the rest - What an attitude!