I've been using stc-1000's as single stage controllers for 5-6 years, running either hot or cold only, with no issues. Cold in my keezer. And currently I have 3 running various hot side only setups- My ghetto sous-vide setup, a "proofing" box for sourdough breads with a lightbulb heater, and my current meat curing chamber in my basement, again with a light bulb heater.
In the case of my sous-vide which is being run off of my original schematic that a lot of people use on here, with a hot, cold and "always on" plug. I run the coffee urn on the hot side, and aquarium pump on always on moving the water, and usually nothing in the cool spot. When it kicks over to the "cool" cycle, everything just goes idle until the temp drops back down enough need the heat cycle back on.
But the one running the keezer I just wired the cold side. And it's run just fine for 4 years or so.