The force magnetic fields apply is always perpendicular to the field: F ~ v × B (right hand rule, and all that). So if you want F to point inward, the one component of B that doesn't matter is its radial component---ie. the tangent component is all that counts. But it's not clear to me that you can't compensate for the restrictions of the hairy ball theorem by having a nonuniform velocity distribution. Of course, there's no "hairy torus" theorem (because it's not true!) and this immediately suggests the tokamak design.

It's also not possible to take a sphere and have the radial magnetic field point inward everywhere (or outward everywhere), because Maxwell's equations prohibit magnetic monopoles.