Nuclear Fusion: Why is spherical magnetic confinement not used instead of tokamaks in nuclear fusion?

Not an expert, but I believe the answer lies in the hairy ball theorem.

You see, for a magnetic field to turn charged particles back from a surface, the field must be parallel to the surface, which means that to have a fully confining geometry you must have a smooth, everywhere non-zero, and continuous vector field mapped onto a surface.

But the theorem say that you can't do that on a sphere (or topologically equivalent shape).

Because that's just one of the many alternative approaches to fusion, and resources are limited.

Nuclear fusion seems very promising, but for all approaches tried so far the challenges have proved to be more numerous and difficult to overcome than initially expected $-$ and the magnetized target fusion that General Fusion has been pursuing is likely no different. One needs to deal with extreme magnetic fields and temperatures, which is hard enough, and at the same time keep a rather fine control in order to maintain stability. That means that too much technology still has to be demonstrated.

Tokamaks and even Stellarators are more mature, developed technologies, so it's natural that efforts concentrate on those designs. That's very expensive research, a long-term investment with returns that are very uncertain $-$ so the alternative approaches have to compete for funding. And once a team has a head start on a given design, there's little incentive for others to follow before it's at least partially proved. That's why these new proposals are mostly being tried each by a single research group.

Background: confining a plasma requires controlling all of an enormous spectrum of possible instabilities. The tokamak does a good job of stirring the flows so that no individual instability can grow so much that the plasma rushes out and contacts the wall (and thus is quenched). Regarding the particular question of a spherical tokamak: the answer just edited above points out that having a field everywhere tangent to a spherical surface is forbidden by the hairy ball theorem.
Magnetic confinement takes advantage of the fact that a charged particle's path is bent in a (strong) magnetic field; particle trajectories tend to be tight spirals about magnetic field lines owing to the V cross B force (Lorentz force): so particles cannot travel across the field lines unless they are scattered out of their spiraling motion. effectively allowing them to jump to a different line of force. For a spherical tokamak we would require an arrangement of field lines which was everywhere strong and tangent to the surface of the sphere. Such an arrangement would contradict the Hairy Ball theorem (mentioned elsewhere in this topic).