I think this is true ("there's nothing wrong with them") if you are talking about an older kid or adult who has skills at receiving comfort from a variety of options, blankey, touch, self-talk, play, other. But in this case, the OP described a young child who had settled into one and only one comfort mode, and the mama saw that this would not continue to serve her child, nor allow her to develop other connections.
OP, I think you're doing great, and you could perhaps go back and edit out of your mind all the apologies and self-criticism in your post. You've watched for but not seen any significant adjustment issues, and you know your daughter is different from meemee's child who can "put on a face." It sounds to me like you finally found the right moment to help her make this change, and congratulations to you for not forcing it on her earlier when you judged she wasn't ready. It also sounds like you're a mama who keeps an eye out, and you'll notice if there's something unbalanced that comes up later. I see nothing awful, mean, wrong, unkind, ungenerous, or self-serving in what you've said here. I just see a mama who is paying attention! Good job.