When you refer to 'case pressure' I'm assuming you are referring to the crankcase compression. Crankcase compression on chainsaws is kept relatively low compared to other two-strokes. The reason why is that a higher crankcase compression will NARROW the powerband.
You can increase the crankcase compression and it will push the maximum delivery ratio of the transfers up higher in the RPM range, however it will also tend to narrow the powerband. Chainsaws need a broader powerband, so lower crankcase compression ratios are used.
Increasing the crankcase compression does not make the crankcase more efficient, that is, it doesn't make it flow any more mixture. Racers have indicated that going to a full-circle crank will push peak power up about 400 RPM. Having the maximum delivery ratio up higher in the RPM range will create more horsepower for cutting cookies and they are willing to accept the tighter powerband for racing.