Is the recommendation for Gauge 14 cables with 13A devices overly conservative?
Many buyers clueless.  Guidelines for extension cord wire size are only adequate for connected equipment and not conservative.

With an undersized cord for the load:

(1) The voltage supplied to a motor will be more than 10% below nominal, causing motor overheating and premature winding failure;

(2)  The cord will run hot causing the cord insulation to fail prematurely;

(3)  The manufacturer warranties of both equipment and cord will be void (if they know what happened);

However, if the utility supplies voltage at the high end of nominal (122v) and the mower is never used to cut thick grass then one will probably get away with using a #16 cord.  The #16 cord is cheaper and less weight to haul around in the yard.  Besides, someone is probably going to accidentally drive the mower over the cord in a couple of months chopping the cord to little bits...