Anthropic arguments only work if there's a mechanism for generating other versions besides the one you're observing. For example, you could use the anthropic argument to explain why earth is in the "goldilocks zone" because there are plenty other planets out there at varying distances from their sun.

So, if you want to make the argument that 3d is preferred for some reason you need to acknowledge that there are other universes out there with 2d, 4d, etc that just can't sustain life and that therefore life only finds itself in the subset of universes that have three dimensions.