Often the wear on the lapped side of the blade is overlooked in the sharpening of chisels and planes. I would guess that there is equal wear on either side of the point. The tip must be ground down so there is no wear visible on the lapped side. This can be done grossly by making the grinding angle quite large so, though it is taking only a small amount of metal, it is quickly grinding the edge back until the wear is gone. Then the grinding angle can be changed to the bevel angle of the chisel is what you desire.

I think the bevel angle is the least important of the parameters of sharpening. Having a flat lapped surface is first. Having any grind that removes the dullness is next. Third is the polish to the cutting surfaces after the grinding operation. Only in special circumstances are specific bevel angles important, i.e. end-grain, soft wood, erratic or contrary grain. 

Having any kind of rounding on the reference surface (the lapped) makes chiseling straight all but impossible. The blade is always having to be tipped up to engage the edge to the wood.