Make a new extension cord really “coilable” for the rest of its life by following this tip when the cord is brand new.
Take your new extension cord out of the packaging, carry it outside on a sunny day, uncoil it and stretch it out in the sun.
After about an hour of this “curing”, carefully coil the cable (here’s a simple video on the best way to do that).
The time in the sun will expand and “relax” the cable jacket, and even after it cools down it will remain much more pliable and easier to coil for the life of the extension cord.