why is it bad if a coax cable (used for antenna cable) has multiple paths to ground?
Coaxial cable "works" because the two currents (center conductor and shield), which flow in opposite directions, are equal in magnitude and share a common axis. This balance is what causes the magnetic field that is produced by those currents to cancel out perfectly outside of the cable. By reciprocity, it is also what makes it immune to the influence of external fields.

As soon as you allow any of the shield current to follow another path, this balance is broken, and the immunity from interacting with external H fields is lost.