Yes, I think this is routinely assumed.You are correct, it is not feasible to have anisotropic pressure and no shear because anisotropic pressure is shear. The only difference is a spatial rotation.
This is assuming that the spatial-spatial part of the stress-energy tensor is the same as the stress tensor from mechanics.
Of course in realistic physical condition neither staticity nor perfect spherical symmetry are expected, and I guess one would have one of the transverse pressure overcome the other and the sphere would rotate ever faster as the mass increased, limited by light speed.
I don't know, anyway it would be interesting if anyone could confirm if a static spherically symmetric SET not corresponding to a perfect fluid is in fact admissible.