The county of Mexico has laws regarding the formation of states that include a minimum population. Cozumel could never become a separate state under present rules. However, the island has always marched to its own drummer. Rules, regulations, customs, and attitudes that are entrenched on the mainland are frequently ignored on Cozumel.
Cozumel has always been a peaceful island. When Juan de Grijalva "discovered" the island in 1518, he was received in a friendly manner, even though everywhere else he went in Mexico he encountered fierce opposition from the Maya who fought him wherever he landed. When Cortes came to Cozumel the next year, he tore down the Maya idols, but they turned the other cheek and helped him fill his boats with food and water before letting him leave peacefully. He even wrote a "letter of recommendation" for the Maya chief to have on hand in case another Spanish expedition came along, so they would know the people of Cozumel were friendly.
I don't know the reason for this peaceful attitude that the inhabitants of the island have always had towards visitors, but it certainly remains a strongly held attitude to this day.
Cozumel is the Mayberry of Mexico, just with a lot more cruise ships.