This lines up exactly with what Dr. Daniel Griffin talked about in the most recent clinical update podcast for TWIV [1]. Apparently aspirating makes the shot more painful, because the needle is in the body longer, and serves no benefit as long as the vaccinator is putting it in the right location.

1: https://www.microbe.tv/twiv/twiv-741/ (towards the end)

"no large blood vessels are present at the recommended injection sites"

That's a bold statement. Sure, no large blood vessels may be present at the recommended injection site on an average human, but it's well known there is more divergence in anatomy than they necessarily teach about in primary school, and vaccines are supposed to go in basically everyone.

Still, even if it gets close to a small vessel it might be problematic

Maybe we'll need to do it for AZ. Or maybe subcutaneous?