I agree, especially when it's your family in the car.Personally I would choose stopping distance over MPGs and day of the week and twice on Sunday. It rains often where I live but not so much in eastern Washington.
I read a detailed road test from Edmunds years ago that pre-dates the development of all-weather tires. But it tested all three types of tires (summer, all-season, and studless winter tires) from Michelin against each other in three conditions: Hot & dry pavement, wet pavement, and snow.
Oddly enough the summer tire significantly outperformed the all-season in both hot and dry conditions. The winter tire also significantly outperformed the all-season tire in not just snow, but also wet conditions! The all-season tire had the least amount of grip in wet conditions. I have been looking for another similar test with all-weather tires, but most of what I find on youtube tire testing (other than Tyre Reviews) is bad testing.
Here is a great article from an actual tire engineer that indicates that all-weather tires are basically just a little bit better all-season tire, and still seem to have the same compromises that all-season tires have: https://barrystiretech.com/winter-and-all-weather-tires/
I'm open-minded about all-weather tires, or at least I'm reserving judgment until I can find the data. I also don't believe they are any good in snow after a couple years of driving -- because winter tires are considered worn out by somewhere between 5/32 to 7/32s, it seems that an all-weather tire couldn't possibly be better than a studless winter tire once it's worn down to the same level. So, consider me open-minded but also skeptical.