You are correct, because we are dealing with alternating current, for a breif time of the duty cycle, the voltage Is insufficient to produce the skin effect. It's worthy of note that power=amps X volts so if your line is at 100kv at peak, and skin effect disappears at (guessing) 10kv, then 10% of the duty cycle is subject to 10% of the load. Which works out to about 1% of overall load actually travelling inside the conductor.
Granted there is a failure point, but without going down a math rabbit hole I will hazard a guess that it would take at least a 1000% load increase above normal to reach critical level.
This is just rough math, I'm sure there are published specs out there somewhere on the capacity of HV lines. It's Sunday and digging sounds like work.
My point being; the power producing stations and distribution substations will fail long before the transmission lines become an issue, since they operate at near-capacity routinely and could not even handle a 100% load increase.
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