Must admit that I have some - possibly irrational - concerns about stovepipe rain hats. Why? Because in all my stove-heated tipis, I've never had even one spark-hole in the fabric, despite running the stoves full-bore. I believe that is because any remaining hot cinders getting through the stove cinder screen shoot out the top of the stovepipe at speed, and either get caught by any bit of wind, or cool sufficiently on the way back downwards to not cause a problem to the tipi fabric. My concerns therefore are that putting on a rain-hat on the stovepipe will deflect sparks/mini-cinders back downwards onto the tipi whilst still glowing. A combination of hot cinder and high velocity seems to me to be a guarantee of burns to the tipi fabric!
And what are the downsides to not having a rain-hat? If the stove is going, even torrential rain is going to evaporate before hitting the stove body. If the stove is out, some water will collect in the body of the stove after a while. No corrosion risk for titanium/stainless steel stoves. Takes a few seconds to mop up before lighting again...