Does coiling an extension cord create a dangerous inductive load?

Not exactly — the inductance from coiling a standard household extension cord at 60Hz AC is negligible. The real risk is heat buildup from resistance: a coiled cord traps heat, and under heavy load (like a space heater or air compressor), it can overheat, melt insulation, and start a fire. So don’t coil a cord tightly under heavy load; uncoil it fully for 10+ amp draws. For lights or phone chargers, coiling is fine.