To me, slashing infers movement on an arc - many slashing swords are curved for that reason. Straight line penetration is piercing. I don't care if there is star of blades for an arrow tip, if the penetration is a straight line (as from an arrow or bolt) it is still piercing damage. Consider that most arrows are not just pointed round tips, rather stone age arrows have "blades" on either side of shaped flat stones of flint. Blades or points, arrows causing piercing damage - hence why D&D has always considered arrows piercing weapons since 1e.
You can houserule that arrows could be other than piercing damage for a home game, but you won't find a consensus of agreement - at least not by evidence of every other post in this thread. We all pretty much agree that arrows cause piercing damage only.
A rapier is certainly a type of sword or bladed weapon, yet it causes piercing, not slashing damage. By your argument, since a rapier is a bladed weapon it should cause slashing damage, which it doesn't, so that should compel you to question your thoughts on "slashing arrows".