Rate limiting would have killed that dictionary. Just the connection speed: 300 baud means roughly 300 bits per second, or roughly 2250 characters per minute.
But what kind of credentials would he have? Would he even gain access to the games he was after?
The whole point of hunting for the Falken backdoor was to gain the highest access he could, so he could get his hands on what he thought were games in development to be released soon.
Also, 'nother WarGames fun fact: Stephen Falken is, of course, a play on Stephen Hawking. At the time of the movie's creation, Professor Hawking had only recently been diagnosed with ALS and was thought to not be long for the world. The original script/treatment was about a relationship between Falken and a teenager, to whom the terminally ill Falken would pass as much knowledge as he could before he died, so his work could live on. When the PC debuted, the script was reworked to incorporate the role computing had in young people's lives, and the nascent "hacker" phenomenon.