There are numerous reasons why someone would want their villager to be original. It's all personal preference. When I cycle, I try to keep the villager as original as possible (in most cases they remain original unless I go several days without cycling, in which case they end up wearing one of those shirts made by someone from anytown lol). I've only done a few cycling trades and have found that more than 75% of those I traded with wanted original villagers (intact shirts, furniture, etc), while the rest didn't mind it as long as they were able to get the villager.
I picked up a void once in my first game, it was Peck, and it took him AGES to forget about his old town (don't even know where he came from to be honest lol). I didn't mind it though as he mentioned it less and less and I rarely spoke to him anyways >.> too busy running around trying to create hybrid flowers. I have gotten Lolly, Rosie and Ankha (all were original) but I wouldn't mind if they weren't. I haven't done any research on what their homes originally come with so I'm not bothered if there's something off when they get to my town. I'm pretty sure I've been guilty of handing a villager of mine a fish or a bug when they asked me to (without knowing this would cause them to display it in their home and maybe sell or giveaway a piece of their furniture).
It would bother me just a teeny bit if I got a dreamie and their home was filled with just fish and bugs though, unless of course I already knew that before then trade, then I'd just gift them furniture to replace all the stuff lol. There was one time when Groucho sent me something I liked him having in his home, I ended up gifting it back to him via a letter and he had it back up in his home xD.
If someone wants original villagers, they have the right to ask for it. Just like if someone is selling unoriginals, they have the right to do that as well. Not one is better than the other in my opinion, afterall, the besides the nature of the villager, you do end up creating them to be "unique" if you change them (clothes, furniture, catch phrases,). My Felicity says "I AM BATMAN" when she sees me
