The article cites the Prosser Report which contradicts this claim, but I find it hard to understand how this could be true for very long. Why wouldn't the atmosphere stabilize as gradients diminish?
Because the earth's rotational axis is not perpendicular to incident sunlight (hence dark polar winters). As winter sets in, gradients steepen relative to warming equator. It's all complicated by the general increase of atmospheric water vapor as warming proceeds, which can have different effects depending on whether the water vapor is gaseous or forms cloud droplets, which reflect sunlight. It's a hard physics problem.