Yes I agree with what Felix says about cot and dummy being linked.
If you're seeing a 3 year old with a dummy (there are exceptions of course) then yes they're too old, I agree with you there. There should be no reason for this, like I say my LO is 18m and no one knows she has a dummy except for me, and her nursery worker. She's never looked after by anyone else, or babysat or has it when we've got social events so it really doesn't bother me.
My LOs dummy lives in her cot, and I've got a trinket box with a couple more in on top of her wardrobe incase one gets lost in the cot black hole! Lol Cot = dummy. If she's out of the cot, she dumps the dummy back inside now she understands this.
I do keep on in the car, and one in the pram on an occasion where she's screaming blue murder ready to sleep but won't drop off like she usually can do with the motion. In those instances they are used but removed immediately on wake up.
I don't, and never have, given a dummy for 'fussiness' or to keep baby quiet so I've never had an issue of overuse, perhaps why I'm so open to keeping it as long as LO needs, but I'd definitely start by reducing it to certain times around sleep and for no other reasons at all.
It sounds like it's not so bad through realy, and if she's capable of finding it in the night (you may need a few more in her bed) then honestly I'd let her keep it.
All this being said with me on the favour of keeping it.....if you did get rid it's really likely to not be that bad in the grand scheme of things. I would do cold turkey (like I'll do when my LO is older, when it's gone it's gone) and battle any issues that come from then instead of tackle small issues do to slow weaning.