That's not the reason why the centre of the universe is undefined.
By analogy, while spherical coordinates are arbitrary, latitude is defined. Arbitrary, but defined.
But the centre of the Earth has an undefined latitude, and a topological subspace consisting of just the surface of the Earth can't hand-wave past that by pointing out that's just a coordinate singularity that can be safely ignored — there isn't a center of the Earth anywhere in that subspace. If the universe is flat and finite (looping), this problem still exists.
And if the universe is unbounded (infinite), that has a different problem because you can't properly define a median of an infinite set[0], so no center exists.
If it just stops suddenly after a certain amount of space, then we get to have a center, but there's no sign of that.
[0] I think. Infinity is easy to get messed up with.
