My understanding is a rain bike is the cheapest bike you can ride comfortably for all your rides on days when the weather is terrible and your main ride would endure unnecessary abuse.

This is not a "jewels vs. tools" thing, it is about properly caring for your tools. Riding in the rain eats bikes, not because of rust, but because fine grit gets pushed into every bearing surface and juncture, from the bottom bracket to every link of the chain, and then grinds away at all your mechanicals. Also, you don't want to be swapping fenders on and off your regular ride after every rainy day.

Plus, it is a reason to own yet another bike (n+1 as was noted above.)

No difficult concepts there.