I clearly misunderstood something
The pneumatic device requires both the correct pressure AND flow rate to work properly. Conversely, the compressor produces a different flow rate at each particular pressure.
If the compressor does not have a pressure and flow-rate combination that matches the pressure and flow rate that the pneumatic device requires, then one of two scenarios will occur if you try to run it off the compressor without a regulator:
If the compressor is too small to run the pneumatic device directly, then the flow rate too low which would reduce the pressure and the pneumatic device would not work properly.
If the compressor is large enough to run the pneumatic device directly the result flow rate would be too high and the pressure would increase, possibly damaging the pneumatic device.
If the compressor is too small you use a reservoir tank that the compressor pressurizes to higher than the pressure you need and then you regulate the pressure back down. You can't run the pneumatic device continuously since the compressor can't keep up, but if you run short enough so that pressure never gets too low and infrequently enough so the compressor can top off the tank you it will work.
If the compressor is too large then you can run the pneumatic device without a reservoir tank but you still need the regulator or else the compressor's will produce a pressure that is too high and a flow rate that is too high and damage your pneumatic device. Of course, you can also use a reservoir tank so that the compressor doesn't need to run continuously, especially if the compressor can produce more air than the pneumatic device uses.
This is very similar to how voltage and current work in a electric load. The load requires a particular voltage and current to function properly. If you expose it to a voltage too high the current that flows through load will be too much and it will be damaged. If the voltage is too low the current that flows through the load will be insufficient. Unless your battery matches the voltage required by the load and can supply the required current without the voltage sagging, you can't run the load off the battery directly. You need a regulator.