Use proper summer and winter tyres respectively and you won't have that issue. And you'll have more grip to go around as well. All season is a pure marketing ploy, only good enough of you haven't tried the alternative.
I'm not so sure that's the case. The Michelin compound still goes rock hard after about 30 K miles. Even if I go to dedicated snow tires, when I put the Michelins back on in the Spring after 30k miles, they'll still be rock hard and have abysmal wet weather traction. So, I might not have poor snow traction, but I'll still be slipping all over wet roads in rain (unless somebody makes dedicated rain tires).
Don't get me wrong, I loved that MIchelins lasted forever, I just hated that they had poor traction (and a noticeably harsher ride) after a while.
That's because you were not using a summer tire for summer. The Michelin Primacy 3 was a summer tire and was wore out at 30K. Same sticky rubber throughout the tread. All Season tires are different than Summer tires. June