Rig one of those 12V accessory plug powered compressors to an impact and tell me how well it works. It can generate the pressure required, but will drop to nothing as soon as you pull the trigger. Why? Not enough flow. A compressor has to be able to generate enough flow (CFM) or it can't maintain a pressure differential. Hence why the compressor/tank combo are rated by their ability to supply a certain amount of air at a specified pressure, and why air tools specify a minimum amount of flow from the compressor to satisfactorily supply them.
Cranking the pressure on a compressor is a band aid for an undersized compressor. It can work, but it's still just a bandaid.
Not exactly. CFM only matters when the tank is empty. A 12V compressor has no tank, thus running a tool relies on CFM. That isn't the case for a stationary compressor for an intermittent use tool.
It is also worth noting that the CFM rating on compressors isn't about how much air can leave the tank- it is about how much air the compressor can put into the tank. So compressors aren't generating "flow." Even the worst 1/4 air fittings have a CFM rating of around 30CFM (which more than enough for any 1/2 impact wrench), so the rate of flow isn't the problem when a gun isn't powerful enough. So why do people see improvements with higher flow fittings? The larger interior diameter creates less friction and thus reduces the PSI less (same reason why a 1/2 hose is better than a 3/8 hose).
Too many people think the CFM of the compressor determines power. It doesn't. PSI is what determines power. When a compressor isn't even running, it's CFM rating is 0. The CFM ratings of compressors are better understood as how well the compressor can maintain a certain PSI.
This is also why you can run an impact at full power (even though the CFM rating under load is 24-28CFM) off a compressor that is only rated at 6CFM. PSI determines the power. If you can't maintain a high enough PSI under load (even intermittent load), then you have a CFM problem. A 2 gallon tank should be able to run the impact a few times for full power before it needs to recharge to allow the gun to operate at full power again.
So cranking up the PSI would make the gun more powerful.
If you truly believe that CFM alone determines power, then I hope you have a compressor that is at least 24CFM @ 100 PSI. Otherwise you wouldn't be getting full power according to your theory.