What people underestimate is the flea-mite cycle: even if your dog has no visible fleas, skin mites proliferate when there's humidity and heat, and trigger inflammation that then amplifies any underlying food allergy. Before switching kibble or dropping money on expensive supplements, make sure you're using a decent monthly antiparasitic year-round, not just in summer. If you're already doing that, then yeah, it's worth testing the diet.
As for steroids: they're annoying for chronic use, but random supplements like low-quality omega-3 often don't do much if you're not managing the environment. What actually works is reducing triggers: dry his paws thoroughly after walks (especially between the toes), use a humidifier at home if the climate is particularly humid, and consider frequent baths with a soothing shampoo specifically for dermatitis. Continuous relief of irritated skin helps more than a lot of supplements.
If you really want to try a dietary approach, ask your vet about a limited-ingredient diet (few proteins and carbs, maybe duck or fish with rice) for a month or two: if it improves significantly, then food's involved. But starting from environmental and parasitic basics gets you results faster and cheaper.