I may not possess the factual potpourri that you do, but I believe that the area you object to was mostly developed by the Parkside Realty Company in the teens, mainly due to the opening of the Twin Peaks tunnel. So maybe "parks" had nothing to do with naming it "Park"-side.
In fact, the Parkside Realty Company named the re-named east-west streets in the Outside Lands from from P (Pacheco) to Y (Yorba).
If I were asked to choose a name for the area you object to, I would suggest South Sunset. It's geographically accurate and completely non-controversial. In fact, there is a playground "out there" called . . . . . TA-DA . . . SOUTH SUNSET