I was discussing this with someone earlier and they were concerned my 3 year old (3y4m if it makes a difference) was wanting to carrying a cuddly toy with him 24/7. They were worried it was an issue as it means he's doing everything 1 handed ie. Eating one handed, drawing one handed etc. They also said he's too old for it now, and he shouldn't need to take it everywhere with him.
I figured we can very easily take the toy from him or get him to set it down to one side whilst doing an activity. But I can't actually see why it's an issue. If he needs 2 hands he uses 2 hands, if he can make do with one then he'd rather hold his cuddly in the other hand/arm.
He forms really strong attachments to things in general. For example his favourite bag of marbles that goes everywhere with him (that he also sleeps with).
I'm going to do a bit of research and chat further with the person. Because I'd like us to figure something out that works for everyone. But until today I'd not considered it was in any way abnormal or a problem.
If you think IABU and you'd be willing to elaborate I'm really curious.