Theoretically you could keep playing forever as long as there were two or more players. The real advantage, however, is that the server can keep everyone in synch and that's very important. There are a few drawbacks, however. If the server hiccups, everyone else gets sick. What I mean is if the server lags everyone lags and if the serer disconnects it's game over.
Many games have a client that is also a server.
The advantage in this is that the game data dosen't have to be loaded twice and a lot of CPU usage is saved, meaning more clients can connect smoothly. Now let's take a look at our space shooter game and see what it will entail. The server should always be ready to accept new login. It should reject new clients if The server is full. Their name is already being used.