Placing orders will always need some kind of infrastructure to optimize the experience and enhance the security. If you knew somebody who wanted to sell you some Bitcoin in exchange for Ethereum, then you could both come to an agreement in price, and make the exchange. Each person would send coins to each other.
That works fine when you're swapping with somebody you know. What about if you don't know the person, and where they live. If you don't trust somebody, you need an intermediary to handle the exchange for safety. This could come in the form of a centralized counterparty, or a decentralized counter party. Big trading firms have wealthy people who want to buy and sell tokens. They match these counterparties and take a fee as a cut.
The DEXs have made it possible for anybody to connect to their APIs and trade cryptocurrencies. We can't do this with stocks, because they are regulated by the SEC. All financial transactions are watched closely to limit money laundering and other illicit activities.
Trading regulated securities is much more complicated than crypto. For that you will need a broker and a clearing house. When you trade, it will take three days to settle a trade (T+2). What the brokers do, is they front you the cash. Then you can sell one stock, and buy another.
Where you have a broker that can sell you cryptocurrencies, and can sell you stocks, then they could effectively give you credit. They could allow you to sell stock, and buy crypto. New companies are springing up everyday to attempt to solve this problem. None have made it big; yet.