But wouldn't it be possible to cheat outrageously in such a game? For instance, what would prevent you from logging into a game simultaneously as three different players, on three different computers each on a different ISP? Wouldn't it be a huge advantage to know what half the cards in play were and who had them?
Yep, especially when the side that could be cheating is also the side running the game. There was no oversight at all into how the games were being run, and a number of fraud issues did occur.