Pour diced tomatoes into a large saucepan or Dutch oven over medium-low heat; add zucchini, yellow squash, eggplant, and onion; stir once. Sprinkle salt over vegetables. Bring mixture to a boil and simmer until the vegetables start to cook down, 10 to 15 minutes; stir in Italian seasoning, garlic powder, and black pepper to taste.
Cook uncovered over medium-high heat until the sauce has reduced and vegetables are tender, about 1 hour, stirring often. (Or if preferred, cover pan and cook over low heat 2 to 3 hours.) Stir in tomato paste and adjust seasonings. Drizzle with olive oil just before serving.
