So far I've never had that request... but I think part of the problem is that people don't want to be educated. Every once in a while we get in a pregnant rescue and end up adopting out the kits - and we will have a mailbox full of responses for one ad for a kit, versus no responses for our ads about the adults for adoption. I educate - I tell people that the adults are calmer, easier to hold, will interact more, and so on... but basically, a lot of the time, the response I get is something along these lines: I don't care, I want the baby or no chin at all.
I personally would rather adopt an older animal. Having experienced owning kittens (which, note, I no longer have) and owning a dog that I purchased as a puppy... I would much rather start with an older animal. Sure, the babies are cuter - the kittens were adorable and the puppy was just oh so cute... but the puppy wasn't potty trained, chewed up a lot of stuff, the kittens knocked over everything I owned, dug in my plants, and were little terrors. Since I no longer have the kittens, I cannot comment on how they are now, but for the dog -- I much prefer my dog how she is now. I often joke that she's a "useless" dog (in the most loving way, it's sort of a running joke) because she can be found lying on the floor/couch sleeping much of the time, and during the time she's awake, she just pads around the house following someone and then plopping down at their feet. I much prefer that, and the occasional play session, to the psycho puppy that I had to watch 24/7 with eyeballs on the back of my head as she dug through my trash and shredded every napkin and kleenex in sight, making it look like it snowed 365/24/7 in my room.
Obviously, chins aren't quite comparable to something like a puppy, but the concept is the same - I would rather go with the older rescue....you at least know what you're getting. But unfortunately, not everyone feel that way - and it's obvious - because I will have deposits down on kits long before they're ready to go, while some awesome rescue chins will sit here for months or years waiting to be adopted.
And a bit more on topic.... I would NEVER want to intentionally hand-feed a kit. While I've handfed my share of kits for various reasons, they were all situations where I did not have another nursing mother and had no other way for the kits to get milk. To intentionally take kits away from mom to handfeed? Forget it. If they need to be handfed every 2 hours around the clock, I'm there. For the heck of it? ooooh no. Not happening. I don't think people often understand what they're getting themselves into when they make requests such as that. The sleep (or lack of) that is gotten for those 8-9 weeks is miserable and I always felt so drained afterwards... I wouldn't intentionally take that on if I could avoid it.