Doing something at random half the time is definitely better than doing it 0% of the time, or predictably half the time. From a security standpoint it's certainly worse than doing it 100% of the time. If you're randomizing day-to-day its pointless though. If you had something in your shoe, you could just walk away once you saw other people taking off their shoes. You're not obligated to continue. If anybody asks then you forgot your phone in your car.
Sure, randomly pulling people over or demanding access to their bank records might reveal patterns, but we supposedly have rights in western countries.
Are you of the opinion that unpredictability has zero security value?