The punch-line, as you've guessed, is that there's not enough time for the ESRB to play every game. That's like asking a chef to make every possible meal before rating a restaurant. And how do you decide when an MMO, or even a repetitive game like Tetris, is complete?
Under the current rating system, publishers provide the ESRB with video of the gameplay and detailed information about a game's content. The ESRB may also play the game, but the group relies most on publishers' full disclosure. If the publisher lies about the game, that company faces fines and the possibility that the ESRB won't rate its future releases. (Most major chains won't stock unrated titles.)
Legislation like this, where our representatives don't understand the subject of their bills, makes us uncomfortable. We hope that logic will end this proposal, but logic seems to evaporate the closer we get to Congressional elections.