I've had AS4s over at Porsche, and they worked fine, or at least seemed to, but I did not test them in any objective way. Certainly I didn't notice a lack of wet traction, and I'm in the Seattle area; they faced a fair bit of wet.
It's an interesting question and I thought it likely we're not the first to ponder it, so I did a quick search. Because we're comparing good summer tires like the PS4 I searched for that versus the AS4 which seems like a fairer comparison than a no-name versus a PS4.
https://toptirereview.com/michelin-pilot-sport-all-season-4-vs-michelin-pilot-sport-4s/
https://www.motor1.com/news/623303/michelin-tire-test-pilot-sport-all-season-snow/
To much typing to try and summerize those and I think anyone that would bother to read what I wrote would rather actually read the comparisons anyway so I'm going to settle for leaving the links.