I've found there are a few reasons why people like playing psionics. The best reason is because it used to be the third type of "magic," with divine and arcane being the other two, allowing for a different option (IMO the sorcerer took this niche away, being the "inner power" source). Early D&D was influenced by Science Fantasy, where the two genres mix, and psionics is a staple for this type of play. A few settings have significantly incorporated psionics as a fundamental aspect of the game, primarily Dark Sun. Quite a few just want to play something weird for the sake of being weird (I personally hate this type of player). In earlier editions there were quite a few who found ways to manipulate the mechanics to gain a lot of undeserved advantages, especially when it was considered to be different than magic (and thus there was almost no existing defense against it).