I agree fully with markbarendt's interpretation and explanation as to the WSDOT flyer posted above.
THE AutoSock must have test results much better than any of the other similar products.
However, in talking with truckers who have used them (I've personally never used them), some of the negatives they mentioned are:
1) they wear VERY quickly once on bare pavement. Many times when traversing mountain passes when "chains required" is posted, there could be stretches of bare pavement interspersed with compact snow and ice. These bare section of the pavement could last a 1/4 mile or more depending on the mountainous region being traveled. Therefore, in a commercial application where a truck is regularly traversing mountain passes in the winter and encountering "chains required," these AutoSocks wear out very quickly and therefore become an expensive alternative to traditional chains.
2) in certain conditions where icy ridges are formed between lanes of travel, if bumping into those ridges accidentally or sometimes when changing lanes, the sock could come off the tire.
3) in the condition where pocked ice forms on the pavement --more common where a section goes un-plowed for awhile-- some have complained that tears have occurred at the seams or even on the main surface area of the sock.
With that said, for a Class A motorhome application, it may be worth carrying these AutoSocks in place of chains since they are an "approved alternative traction device" that can be considered a chain-substitute in the majority of states (I believe I read that they are approved in 45 states but I'm not sure if that's only for passenger cars or if that also pertains to heavy trucks, buses, motorhomes, etc.).
To address the OP's opening post, yes, I personally believe you should consider the AutoSock as you are required in most mountainous states to carry chains or an approved alternative traction device on-board while going through designated sections of highway in the winter months ...whether you use or intend to use them or not, you MUST carry them on-board according to law.
As others have said, if it's bad enough to have "chains required" posted, most of us will just pull over and wait it out. After all, you have a house with you. You can relax and watch TV, read, eat, nap, etc. while waiting. If on an interstate highway, typically "chains required" situations will not last too long. Sure, sometimes there will be times when an interstate is closed for a day or "chains required" is up for hours and hours but that is not the norm. Interstate highways are priorities to be kept open because of commercial traffic and all states do their best to keep them open during adverse weather conditions and keep them closed for as little time as possible.
Pertaining to chains, if you do choose to use them, make sure you have enough clearance in the wheel well area. Many Class A motorhomes do not have the clearance to run steel links. And if you do have the clearance and choose to use them, keep in mind that if a link breaks or you don't secure your fasteners or excess linkage correctly, you may do very expensive damage to the body of your motorhome ...fiberglass, paint damage, etc.
And not to mention getting steel chains or cables wrapped around in the space between the duals and having to hassle trying to get them untangled or cut off when it's freezing cold, snowing, raining or freezing raining ...don't ask me how I know.
Bottom line, as most of us profess, just pull over and wait it out under "chains required" situations.