my little niece just has a "rag" - basically an old spew rag or a small hand towel - doesn't matter what type, just so long as she has something to snuggle up to - she's even stayed here and stolen a face washer from the clean washing and gone to lay on the couch for sleep! her big brother was a "tag" boy - you could give him anything to snuggle to go to sleep, as long as it had a soft tag on it! he'd lay there and just rub the tag on his face til he fell asleep - even now (he's 5) - he'll sit there watching TV with a tag rubbing on his face!

i don't see it as a drama at all - if it gives them comfort and helps them settle in unfamilar environments, why not?