I'd be interested to see any mathematical or economic proof you can back that statement up with.
Not sure if serious.
IN case you are serious, assume reinvesting would somehow increase your share of the network. Keep doing that, see what happens. You would end up with >100% of the network. The same logic dictates that if several competing mining companies reinvest their revenue, on average, everyone loses. Well everyone except the network itself. Welcome to the zero sum game.