There is no "need" for the world to be the way it is - it just happens to be.
Sort of. But this is a weakness with your model.
You can't explain why the earth is flat, in your model it just happens to be so.
But mainstream science
can explain the shape of the earth.
The earth
does have to be a sphere because of gravity.
This is why all objects above a certain mass are spherical.
And science can explain the oblateness too, when a non-rigid body (as the earth was when it was forming) is spinning the centripetal force will make it bulge around the middle.
The original question should be not why does the north pole "need" to be in the centre - as you say, it doesn't
need to be, it just happens to be. Like the UK doesn't
need to be separated from Europe by water, it just happens to be (although hasn't always been). A better question is why do you
believe that the north pole is at the centre of the flat earth. And I'd suggest the answer to that is because Rowbotham lived in the northern hemisphere. From that vantage point one can observe Polaris stationary (more or less) above the North Pole and other stars rotating around that point. So it makes sense, if you're going to create a FE model, to make that the centre. But if you're in the Southern hemisphere you'd see stars rotating in the opposite direction around some southern point.
It's speculation, but not baseless, to suppose that had Rowbotham lived in Australia he might well have made a FE model with a southern hub in the middle. The problems your model has with distances and observations of sun movement in the southern hemisphere would then exist in the northern hemisphere. This would be a bigger problem given that 68% of the land mass and 90% of the population is in the northern hemisphere, but that doesn't mean the problem doesn't exist with the North Pole being at the centre.
The fundamental problem is the same one cartographers have. How does one represent a globe earth on a flat plane? And the answer is there is no way perfect way of doing so. The projection most often used makes Greenland the same size as Africa, which it isn't. You can fix that with other projections but you're trying to fit a too big carpet into a room. You can flatten down (pun not originally intended, but I'll take it) one corner of it, but another corner is going to pop up somewhere.