While I generally agree, some names aren't meant to be proper names, but actually the meaning literally written. Those work better if translated. I mean, Fluffrir sounds dumb as fuck, but that's what the original sounds like in Japanese, and that's the author's intention. Mofurir doesn't work unless you know enough Japanese, and if you have to add a translator's note then the joke's already failed.
So yes, there is a reason to translate some names. But they're generally rare.
I think the main confusion with Lyuu to Lew is that the former is two syllables while the latter is one, so the difference appears to be greater. It's not like anyone (that I've seen) care of you write Leila or Layla. However, it's a different problem, as that's more about how you transcrible リューイン, as Lyuuin or as Lewin, and both are valid, and which people got used to first.