Curl of a magnetic field outside a wire = 0 even though it decreases with radius

Outside an infinite length wire of radius a with even current distribution, the magnetic field vector for such a field would be

begin{cases}
frac{mu_0Ir}{2pi a^2} hat{theta} & rleq a
frac{mu_0I}{2pi r} hat{theta} & rgt a
end{cases}
Mathematically, this would mean that the curl would be 0 everywhere outside the wire.

With my limited understanding of curl, I thought that as the strength of the field decreases with distance, that would mean that the varying strength would result in a net curl that would form at some point outside the wire.

Why would that not be the case?