It's even more strange than that when you consider that the UK hasn't been any sort of industrial manufacturer for many decades. What is it that is supposedly being shipped? Granted, some British auto manufacturers might be shipping those, but why should containers full of phones ever leave the UK? Every ship leaving their ports is leaving with stolen goods.
If anyone cared, this problem could be ended even without the cooperation of the destination countries. But no one hurt by this has enough political sway to do anything about it.
The UK exports a reasonable number of cars (I think less since Brexit now they make less sense going to Europe). Also machinery/technical equipment, pharmaceuticals, alcoholic drinks, clothing, furniture, etc
To appreciate why, consider strips along two constant latitudes. One along the Equator and the other very close to the pole. The uniformly random polar coordinates method will assign roughly the same number points to both. However the equatorial strip is spread over a large area but the polar strip over a tiny area. So the points will not be uniformly distributed over the surface.
What one needs to keep track of is the ratio between the infinitesimal volume in polar coordinates dphi * dtheta to the infinitesimal of the surface area. In other words the amount of dilation or contraction. Then one has apply the reciprocal to even it out.
This tracking is done by the determinant of the Jacobian.
This gives an algorithm for sampling from a sphere: choose randomly from a cylinder and then project onto a sphere. In polar coordinates:
Potentially this is slower than the method in the OP depending on the relative speeds of sqrt and arcsin.