I don't think it's idiotic at all. I think it's plausible that he could've just impersonated him for that scene just to hear what Thor had to say about his dead brother. It would've given him great delight and he could've scoffed to himself secretly later on. It fits with Loki's character.
Hasn't he impersonated various people from time to time? And so have other comic characters as well (eg the Chameleon, Mystique etc). Doesn't always mean that the person they're impersonating is dead or kidnapped at that point. Maybe they're only assuming their identity temporarily for a particular purpose (eg to gain information, to fool someone for whatever reason etc).
And if it isn't Loki, then that changes the whole reason for why Odin would want Lorelei back. If it is actually Odin, then it's purely to retrieve her, but if it's Loki, maybe they're setting her and Amora up for Thor 3.