Most innovation is done by workers working for some company, no? Product development, research, etc is usually done by workers for a salary, not because they're competing against someone. Competition is not needed for paying people to improve things.

Competition has a lot of negative effects as well. Competition by definition has losers. Competition leads to resentment and conflict. Competition forces people to do things they might not want to to survive, because the moment someone is willing to do something to get an edge, everyone is forced to.