I would allow it in my game, but not with the Increased Reflexes power. Not EVER. No one gets a PP 2 power to give +3 REA dice and +3 IPs. I'ma hit any player that tries with ALL of my rulebooks, including ones from older editions.
It looks cheesy, but he can still get Increased Reflexes 3 and some other fun implants for the same amount of essence (and a lot of money) - without any restrictions on his power, or need to spend a 10bp quality. Put in that context, I'm not really seeing the problem... in fact, I'd be all for it.
Or you end up getting bonus style points for shooting enemies while moonwalking...
My man. Enjoy your extra positive rep.