The host and peripheral PHYs are different. Protocols going downstream and upstream are different. USB peripherals are literally not allowed to speak unless spoken to. It's always the king and his slaves. It's that way in the hardware.

You can make such a standalone computer, painted in orange and marketed as an ice cream, that works as the king class when a slave-class is connected to its sole USB-C port, and as a slave class when a king-class like a laptop connected to it. This is in fact how many smartphones work. But that's again not what you asked.

Exactly what you're asking in the way you're asking, standard USB protocols(and DisplayPort signals) going in and out of devices and computers freely like Ethernet packets, just isn't possible with USB.