Mostly history. Numbers were chosen rather than other identifiers because they were simpler to use over the wire back in the day when the protocol was written when every bit cost, and nobody at the time could imagine a single physical machine managing more than 65535 programs at the same time, since that was how you conventionally hooked things up. The IANA (International Assigned Numbers Authority, https://iana.org/) is responsible for maintaining a list of "registered" numbers, but those are largely by convention, not by requirement. Web browsers associate https traffic with port 443 by default, but as a developer, we can set up a webserver on port 50443 and send our browser to if we specify that number explicitly. It just wouldn't know about it by default.

Nowadays, with virtual machines, NAT subnetworks, and the absurdity that is involved in port-per-transaction networking (We're looking at you nginx proxy frontends), it's gotten a bit congested. Fortunately, IPv6 has relieved quite a bit of that, and we now have a much larger pool of 2x(IP/Port) quads to draw from, but it was a real issue there for a while.