1D and 2D are just mathematical abstractions.

So are all dimensions. The number of dimensions is just an attribute of a vector space, and vector spaces are just models we humans define to describe natural phenomenona. You can claim that some of these models are more useful than others. But at no point does it make sense to claim that a model “exists” or not. There would be no meaning to such a statement, it would contain no information. Not wrong, just nonsensical.