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Your point is a very valid one. Using squares on a battlemat creates strangeness like you described.
Note that I edited your diagram and added another orc at Q. Note that this orc could also avoid an AoO from P by moving 5' to the east, then 5' diagonally southeast, then 10' diagonally southwest to get adjacent to P (that last step is identical to the last step that H would have used moving in a straight line to P).
Awkward, isn't it?
In this case, you can do one of several things:
1. Play it by RAW Squares: Moving from the unthreatened 15' square to the unthreatened 5' square doesn't provoke since the orc never leaves a threatened square. Silly, gamist, but RAW.
2. Play your reach weapon to sometimes be 15' long: Allow the reach weapon to hit the four corners even though they are 15' away, but then make sure not to allow it to hit any other squares that are 15' away. Silly, gamist, but it plugs those holes.
3. Play it by RAI squares: The reach of that polearm really covers a doughnut shaped ring around P, and even though RAW squares have 4 holes in that ring, RAI tells us that the ring is a solid 360 degrees around P. So even though a path via squares can be found that avoids provoking, we know that these orcs really do have some point in their path where they are 10' away before they move...
4. Use a hex map :P