It’s an interesting thing to think about - I would argue that you have a point, but unlike economics, which is by definition social because humans are fundamental to the economy - statistics can be focused on non-human subjects across the natural sciences. But, when statistics is applied to humans and societies e.g. through sample surveys, I would argue that in those situations it is operating as a social science.

I’ve not delved deeply into the definitions around this, my work is usually in programme evaluation in the development sector, but I’d be interested to look up academic writing around this question.

I’m unfortunately one of those crazy people who is genuinely enthusiastic about the philosophy of science and abstract definitions.