I have been involved in a telephone equipment addition that upped the power consumption to the point that the triplex burned off at the mast head. My question is "Can a visual scan of the entrance give a clue as to its capacity?" Where do the power company engineers get their specs?

Power Co. engineers, or planers as they are called here, get their “specs” from the engineered drawings done by a registered engineer. They look at what the actual demand will be, not the connected load, and size accordingly. They always tend to size to the low end to reduce cost. If you added a considerable amount of load to this facility you could have very well exceeded the capacity of the utilities feeder without exceeding the actual service equipment rating. Hard to tell without more info.