If they get too close, they could flash over. Additionally, they are more likely to physically contact from things like wind, nearby car vs pole accidents, fault current flowing through to a remote location or differential ice loading.
One other factor to consider is construction consistency. In vertical construction, just a small difference in tension between two phases can result in a pretty significant difference in sag.
What do you mean by induction? Changing the phase to phase clearances would change the impedance of the line, but that is different from a three phase power line causing induction in some other nearby cable.
In some instances, we scale up the clearance listed for distribution voltages for our transmission system. In others, it is based on standard lattice tower designs. In long span crossing applications, each one is evaluated separately.
Utility is areas with raptor problems sometimes have phase to phase spacing large enough to prevent the birds from touching two phases at once.
Mark