Never thought about it. I guess that once you accept the idea of spending hours riding in the rain, the issue of walking it it isn't much of a factor.
Also, On tours, I carry a waterproof(?) shell for riding, and use it when walking also, reducing the need for an umbrella.
FWIW, I tour light, so EVERYTHING I carry has to me multipurpose, or used routinely, or otherwise "gramworthy". So, an umbrella wouldn't make the cut, except as a way to prevent rain in accordance with Murphy's Law.
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WARNING, I'm from New York. Thin skinned people should maintain safe distance.