Is mobile data more reliable than my resort's Wi-Fi (e.g., at Park Hyatt or Four Seasons)?

Yes, for mobility and price. Most luxury resorts (like the Park Hyatt on St. Kitts or the Four Seasons on Nevis) charge very high fees for "premium" Wi-Fi, and it often only works in the lobby or room. A personal eSIM gives you a private, fast 4G/LTE connection that works everywhere, by the pool, on the beach, and, most importantly, when you leave the resort to explore.