More or less skid patches for winter tires?
To spread skid patches around the tire, you need to have chainring and cog that have mutually prime tooth counts, i.e. no common divisors. With a common 42 tooth chain ring, 21 is the worst possible choice because it produces a straight 2:1 ratio. If this did no seem to make sense, search for "skid patch calculator" to find interactive visualizations.

If you really want to avoid excessive tire wear at the cost of some style points, a front brake is great. Also, the current version of Schwalbe Marathons doesn't seem to wear that well.

Edit: After writing the answer, the question has changed. Having less skid patches is a good idea, if your aim is to wear the tire to cords faster. It will not help with braking because the tire has skid patch facing ground when you brake. It will also not help much with lateral grip, because the smooth patches will be even smoother.