I'm not sure if exhausting ports would be the issue. Other services that do just this such as WebRTC SFUs. With 65,535 ports available that your talking 30,000+ concurrent TCP connections.
However, with that many users first obvious problem would be memory. At 10 mb just to start up PHP, that would be 300+ gb of memory without including a single line of code or actually doing anything. If your working with a seriously trimmed php binary you can get down to 4 or 5 mb, so at 5,000 concurrent users you would have around 25 gb.
But the real problem is that it would result in thousands of processes, which is impossible to work around. This would be entirely wasteful considering ReactPHP's eventloop can handle 10k users within a single process. Not saying a single PHP process can do the work for that many users (except maybe the most basic chat) but ReactPHP can handle the IO. Throwing them all into their own process though would a nightmare.
The basic idea has been tried in other languages by giving each user their own thread, but even in C/C++ this is quickly proven to be a bad design.