Can I use a retractable extension cord reel for continuous high loads like a space heater or refrigerator?

No, not unless it’s a commercial-grade reel specifically rated for that, and even then I’d think twice. Heat builds up when the cord is coiled, and most reels use 16 or 14 gauge wire too thin for sustained 15-amp draw, plus the spring mechanism adds resistance. Heavy-duty 12-gauge reels exist but are expensive and meant for temporary workshop tools, not permanent appliance connections. Reels are for temporary use, not 24/7 loads.