I suppose running Bitcoin Core without port 8333 is useless for the network, is it?
I wouldn't say that it is useless, at least you're doing more than most. Per my understanding, port 8333 is meant for inbound connections which is the channel that allows other nodes to connect to your own node but in the event that you are not able to open the port, you still provide the network with some benefits
The Bitcoin network does not only check port 8333 for P2P connections. When it gets the list of peers from another node, or in the case where there are no other known nodes, then from hard-coded seed nodes, it receives the port number along with the IP address.
That way, you are able to set the listening port to be whatever you want it to be, and still receive incoming connections as long as your network is configured correctly.