You can not eliminate the middle man in businesses, especially in this digital age, be it fiat or cryptocurrencies, because they have come to stay. Big exchanges like Binance, are cashing in on being the middle man in businesses, an unavoidable indirect business associates, in your face, waiting for you to go through them.
Going by what p2p is, we can make use of decentralized exchages as well in getting our needs, centralized exchages to some is the last option they could recommend in which one can use to acquire bitcoin which isn't, however if we must then use any, there must be this understanding that our asset must be moved to a personal wallet for safety, some actually depends on these middlemen functions to earn a living because that's how their own way of making business comes in, we should know that we can also do without them in cryptocurrency.