Why don't globular clusters flatten with a galactic disc?
Globular clusters formed whilst the gas of the proto Milky Way was still approximately spherically distributed.

The gas forms a dissipative system that loses energy and collapses (within the first billion years) to a disk whilst conserving angular momentum.

Formed stars and clusters are essentially collisionless so the halo stars continue to have a spherical distribution, whilst more recently formed stars formed from gas already in a disk and so continue to be in a disk.