Here's the thing. Suppose you design a game. Your game just happens to be the most awesome game ever. But it only works with multiple players. So you host your game online and set it up like a spider web waiting for players to log in and get hooked. The problem is that people log in, look around, find no one to play with, and then log back out.
Now, suppose instead of designing your game for multi player, you designed your game for single player, but with multi player support. Now you host your game, and you find that people logging in get hooked on the single player aspects of the game. These may only be fun for a little while, but as long as it keeps the players engaged long enough for other players to show up, then the multi player aspects begin to be visible, and the players will continue to have fun playing the game with other players.
Poor me, no one to play with.
A lot of the BYOND games that I've seen are designed purely for multi player. There is simply nothing for the player to do unless there are other people to play with. No one plays these games. No one plays these games BECAUSE no one plays these games. If these games could keep players occupied while waiting for other players to show up, then suddenly there would be other people to play with.
Furthermore, when you allow people to play single player, you allow them to develop an interest in the game on their own, and this can result in the creation of small gaming communities. People getting together to talk about the game. If these games have multi player support as well, then these communities can serve as a means for people to get in touch and find other players, or perhaps set up hosting schedules.
The bottom line: build single player games! Even if what you truly want is a multi player game, giving it a strong single player aspect will help your game to get off the ground!