For me, the only thing that has contributed to tannins/harshness was the fine particles. A little bit of protein/cloudiness in the runnings is no worry for me (full disclosure - I don't do delicate lagers).
I do batch, less than a quart of vorlauf, and use a double strainer after that for any more that occurs when I open the valve wide open. Sometimes I've gotten a few particles in the strainer, which is why I use it. Hard to know for certain every little process change that affects flavor, but why screw with perfection?
(I love my beers better than any micro brew these days)
But the point is that the majority of stuff that will cause some issues you can actually taste is in the first quart, even for fairly fine grind batch sparging.
As a side note, if BIAB works well, it seems like just lining the cooler with the same filtering bag and just opening the spigot full bore right away would work, assuming the first little bit of hazy protein in the vorlauf would not affect flavor. But to trade 5 minutes for sparging for 5 minutes of cleaning the bag - not gonna happen.