Wait a second? Isn't every transaction on every exchange a P2P transaction? We actually sell to someone who wants to buy it then what's the difference that you are talking about?
Centralized exchanges offer their services to trade and not the blockchain. They keep records on their own centralized servers. They don't sent transactions on the blockchain for every trade. Imagine every trade having to be permanently recorded on the blockchain. That would be totally confusing. The fees we pay to trade on CEX's are not miners fees. Withdrawals only contain miners fees.
P2P means no third party is involved, or its involvement is strictly about facilitating the P2P trade by bringing together a buyer and a seller (by listing their offers) and perhaps performing escrow services (which are acting as third party though).