So, the amount of energy available from complete combustion of a given amount of fuel in oxygen is constant. You can't do better than complete combustion, so having too much oxygen means less than optimal performance. Likewise, having too much fuel (for a given cylinder size) means more incomplete combustion, and also less than optimal performance.
Now if you use N2O as your oxidant instead, you get even more energy, since you're essentially getting the original energy plus the energy from the decomposition of N2O into nitrogen and oxygen. So using nitrous as an oxidant increases performance in itself, as well as increasing the amount of oxidant/volume in your inflow and allowing you to use more fuel for a given cylinder size.
Now your question seems to be: Why not add pure oxygen and more fuel instead? Well, that would work, but you'd only get the latter benefit.
It's also impractical. Oxygen can't be stored efficiently. Oxygen has a boiling point of -182C, nitrous oxide −88C, and oxygen has a much higher vapor pressure. I.e. in practice, oxygen canisters contain compressed oxygen, whereas nitrous oxide canisters contain liquid nitrous, and thus store much much more gas per volume.
So not only does nitrous oxide give you more energy than adding O2, it's also a lot more practical to do so.