I got into an argument with a guy, an industrial engineer of all people, who insisted that the the probability of a coin flip after 5 straight heads was hugely in favor of tails.
No, it doesn't tell you those things, but that's why it's only one of a myriad of stats. The others are where you look for answers to those questions. The utility of pyth is exactly as you state it, and, to me, that kind of information is useful when looking at teams heading down the stretch.