Online play changes things. (Score 2, Insightful)

It is reasonable to have it in a multi-player game where players are logged into a central online service. Ladders and ranked play require some transmission of game statistics to function at all. Since we require a mechanism to transmit that data, we can gain a lot by extending it to capture detailed game statistics as well. The types of games that require public betas are usually online multi-player games that fit the above criteria, and the need to continue monitoring that data won't go away once the game ships. I'm not sure of a scenario where a developer would publicly beta a game that wasn't an online title, so I'm not sure where your above mentioned scenario fits in the real world.