In physics, it is sometimes asked why there should be just three (large) space dimensions. No one really knows, but there are various mathematical properties unique to three or four dimensions, to which appeal is sometimes made.
I would also consider the recent (last few decades) interest in the emergence of spatial dimensions from entanglement. It may be that your question can be answered by considering these two things together.
In physics, it is sometimes asked why there should be just three (large) space dimensions. No one really knows, but there are various mathematical properties unique to three or four dimensions, to which appeal is sometimes made.
I would also consider the recent (last few decades) interest in the emergence of spatial dimensions from entanglement. It may be that your question can be answered by considering these two things together.