The Gem. asks 'what does the Mishna exclude by writing down the count'?, (we could easily count it ourselves).
But the Mishna, before it was written down, was to be learned and memorized and remembered by heart. Isn't it easier to recall all the items in a long list if one knows the number of items that one has to remember?
So how could the Gem. ask 'Minyana Lemiutey may'; it wasn't meant to be 'memayet' anything; perhaps it was said this way, so that it should be easily memorized and repeated!
Kol Tuv
alex lebovits, toronto, canada
I think that Rashi is addressing your concern when he states that the number "implies only fifteen and nothing else." If there were more than fifteen, then citing a specific number could make someone memorize a mistake, making him think that the Tana held that there were only fifteen when in fact there were more. Even if the Tana wanted to write "fifteen" for memory's sake alone, he couldn't. Therefore, if the Tana states that there are fifteen, this must mean that there are only fifteen, and all other possibilities are incorrect. ["Minyana l'Me'utei Mai" doesn't necessarily mean the benefits of memory are being ignored, just that fifteen could only be said if nothing else is correct. The Gemara therefore tries to find out what else would have been counted (and is instead being excluded) had the Tana thought it was in this category.]
All the best,
Yaakov Montrose