They help. Last frozen spigot issue I dealt with was with a "frost-poof sillcock" (the long faucet that has the valve on the inside) and it probably would not have frozen if it had one of these on it.
Those are supposed to work on the principle that the valve and water are on the inside of the building, but in very cold weather the exterior part still gets cold, and the exterior cold conducting in along the metal pipe exceeded the interior heat conducting out, so the pipe attached to it (on the inside, beyond the valve) froze anyway.
One of these covers significantly reduces the rate at which the outside part conducts cold, so it can tip the balance. If you prefer, it reduces the rate of heat loss from the outside faucet, retaining more of the heat conducted from inside along the pipe (same thing, said differently.) Heat comes from the inside of the building being heated in winter.
I fixed that one by the traditional method from before "frost-proof sillcocks" (perhaps better referred to as "frost-resistant") of putting a valve with drain further back along the plumbing. Both methods require someone to remember to do something with the faucets before winter, which can be a problem.