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Brushless motors in RC tend to be huge if you want them to have enough torque, instead of speed. I would presume you couldn't get around that in something that would fit *inside* a gearbox the way you're describing. You never know though, even if it reduced the need down to a single gear connection, it would still be better / quieter / less complex than what we have now.
Still, since our guns are already several pounds, we don't really need the electrical efficiency gains from going brushless the way RC aircraft do (they need smaller / lighter batteries). And as for reliability, as far as I know, lots and lots of other things typically break down in a gun long before the brushes wear out.
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