Why not inject Oxygen instead of Nitrous Oxide (NOS*)?   

There are LOADS of reasons.

a) When you compress nitrous oxide gas into a bottle it goes into a liquid - It collapses. Its a bit like looking through a clear cheapo cigarette lighter...  With its own vapour or "gas" above holding it in this state. Liquid is hugely more dense or compact than a pressurized gas can be. So It takes up massively less space than compressed gas does and solves its own storage problems.  It also means that the bottle pressure never changes as the content level varies. Its sits there in perfect equilibrium. as long as there is at least some liquid Nitrous left. Only the temperature can change the pressure.
 

So that means that a bottle that's almost empty has the same 800 psi in it at room temp as one that's just been filled. We can then jet the nitrous system in a simple way and get a consistent liquid nitrous flow regardless of "how much is left" in the bottle as long as some is!

It boils off and restores its own 800 psi at room temperature pretty damned quick no matter how fast we use it up or leave it stored. It keeps itself liquid just like LPG or many other gasses. 

An Oxygen atom (technically O1) cant live on its own it gets lonely. It combines with itself. So really its O2 (or for short periods O3 or Ozone if you prefer but it prefers 2 atoms because 3 is a crowd but it cant live just with itself it gets lonely! Weird or what)

Now O2 or Oxygen as we know it cannot be compressed into a liquid. This causes huge problems. You have to cool it really cold to get it liquid. Now you can keep it liquid by allowing it to boil off slowly like you see on TV with liquid nitrogen. boiling away... Or like NASA did with the moon landing Saturn Five Rocket.
A bit impractical for a car...

But you can compress it. Unfortunately as you use it the pressure then falls off fast. So you need a regulator and regulate the gas that comes off at whatever fixed pressure you choose. But it better be a big regulator! You are going to need a lot of this gas.

Now even a BIG bottle with say 3000 psi of compressed oxygen in it is still very little actual Oxygen compared to the amount of oxygen stored in a small bottle of LIQUID nitrous oxide.

b) We inject LIQUID nitrous oxide at a controlled rate via a jet into the intake system. Here it starts to absorb heat from the air in the cars intake system causing MORE AIR to be drawn into the intake due to the rate of contraction and cooling of the intake air. At least in sane power output settings!  So manifold depression actually increases at the same time as you are adding more oxygen! Clever trick. And at the same time the charge is drastically
cooled. To way cooler than any intercooler could ever achieve! This charge cooling and manifold depression increase along with increased charge density is where much of the extra power and anti detonation property comes from.

Introducing gaseous oxygen instead does two things... If you could add enough to get any appreciable power increase it takes the place of the incoming air via the carb/throttle body. Because its not liquefied. So its "bigger" physically than the nitrous charge.

On the face of it not an issue. But unlike nitrous oxide which:

i) does the opposite,
ii) cools the charge massively. But that's not the worst! That bad bit is that it both "blocks off" the nitrogen cooling in the intake and contains none itself.

c) consider what happens in the combustion chamber. With nitrous we have the
Nitrous Oxide compound in very cold dense form (no free oxygen here until AFTER compression / combustion!) and we have the normal air (plus a bit extra since its
now ice cold) and the fuel. Under compression nothing happens until the
spark.

Then as the normal ignition process of air (oxygen/nitrogen/fuel) takes place the NITROGEN absorbs the heat and expands and because the Nitrous oxide compound doesn't split up until after ignition then the initial charge that's compressed and then ignited is over rich too.  At this time the Nitrous oxide compound splits! Then it releases 2 nitrogen atoms and 1 oxygen atom from every N2O compound molecule. So now the freshly released oxygen can oxidise the remaining fuel. And its all very safe and actually helps prevent detonation.

Now try this with Oxygen instead! You have very little nitrogen. You have the fuel. And you have a warmer charge that's very Oxygen rich BEFORE ignition. Under compression any tiny glowing particles left over from the previous combustion cycle, or a hot valve or plug electrode will cause ignition! Very early!  And very quickly. Effectively you will run over your own crankshaft. Ever play oxygen on to a bit of hot metal? Or watched a science teacher relight an extinguished taper by dipping in a test tube of oxygen? Its not what you want happening before the spark! And even if you don't run into those problems there are more!

d) After ignition you will have horrendous heat problems. Think melted. Because... The Inert Nitrogen (78 percent of air and 64 percent of the split up Nitrous Oxide) is absolutely essential.

It is this that prevents the horrible detonation and runaway heat problems that your car would have by absorbing the heat generated and expanding to shove the piston down. It is the most abundant gas in the combustion chamber. And it really does need to be. And remember that the BULKY gaseous oxygen that you add to your engines intake system actually displaces the nitrogen that would have entered by the throttle plate.


Incidentally I tried it anyway with the oxygen gas from a welding torch on
an unsuspecting 125 Honda. Sounded awful and emitted many sparks. Good job
it wasn't mine...

*Technically the term NOS is incorrect as this refers to an specific company (called Nitrous Oxide Systems, in the US)