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No, I don't think you can have your cake and eat it too. But there are options.
In Japan these umbrella handlebar mounts are very common, or biking while holding an umbrella with one hand. It works okayish, it's comfy but only if your ride at a leisurly pace.
Ponchos are another good option for tropical monsoons and they allow ample airflow underneath.
The best option is bicycle specific rainwear. Has vents. and is designed to fit just right. I commuted in such attire many times although desu it was always rather chilly when it rained so overheating was never an issue.
