I personally feel anxious every time I change lens
Don't, there is no need, unless you are in some harsh conditions.
I had my Olympus cameras mounted on a telescope for hours on end, in various conditions (warm, cold, freezing, dew, stuff like that). With a Newtonian telescope, there is nothing between the sensor and the environment. Yet, I have not had to do sensor cleaning for all those years. Magic?
There's a picture on the front page right now that shows the new Fuji sensor. I can feel all the dust landing on that unit. I can only hope it was cleaned afterwards.
That's what in-camera sensor cleaning takes care of. I don't know if other camera brands have such a thing. But I don't care. Olympus has it, so dust on sensor is something that happens to others, not me.
It's not that having the sensor exposed when the lens is removed is useful in anyway, so why do it?
Oh, it is useful. Can you imagine paying for replacing a shutter every time something touches it by accident or some piece of debris gets jammed in it?