Coax can arc/spark lightly if your phone service is thru the cable and someone rings the house while you're connecting it (100V ring voltage), tho that will not be the cause of a burned cable.
Coax is grounded back to the service panel via the 1st splitter. Cable Co shares POCO ground on pole. Split phase service, neutral carries imbalance of current back to the xfmr. Normally the neutral is in good condition and carries all of that current despite the parallel path. Lose the neutral (and w/o a metal water pipe bond) now all the house's neutral current goes thru the neutral ground panel bond, onto the ground system, to which the coax is tied to via the #14 solid bare ground wire that's usually there at that 1st splitter, across the outer braids/shield of the coax back to the common xfmr/Cable Co ground to the xfmr, and that thin foil and braids is gonna carry maybe 10A before it smokes. That's also why the coax doesnt smoke after that splitter (on the customer side); the #14 ground wire is carrying the imbalance of the current and a free air #14 wire is good for probably 30A. The choke point is that splitter and the coax shielding.
The article I cited doesnt quite mention the complete pathway as above.
eta: for this exact reason is why I do not like tying the coax to the building's GES. A separate rod at the cable demarc like they did 30 years ago will shunt a lightning strike just as much as tying to the GES will (probably better given the extremely short run of #14 to the local rod). If you lose a neutral you will not fry the cable. Continental Cable Co did every house here in the 80s like that and I've never seen problems of any kind with that setup.