Psionics outside of divination is post-modern philosophy and archetype, and doesn't belong in past-modern fantasy genre.
Your idea of psionics as divination actually comes from the ideas of 19th and 20th century spiritualism. Historically, divination was a divine or diabolocal province, as only God could see the future or the Devil use false images as temptation.
D&D is very much a modern fantasy genre. If wizards worked like the beliefs of the past had them work, they're have almost no resemblance to a D&D wizard at all. Historically, very few wizard even had the reputation for creating mass damage spells at will. Everything was done via ritual preparation, and about the best they could manage in the direct-damage area was summoning a killing storm or other natural disaster. Usually they'd go about cursing or souring people's luck, or giving them some incurable disease. Merlin is almost unique in the annals of human storytelling for the array and power of his abilities.
D&D's ideas, look and feel come from fantasy novels. Several have already been mentioned, a number of times, as works that either use a psionic system in place of a magic system, or combine the two. I'm not exactly where you come about this idea that psionics are 'all powerful' but it seems that you're forgetting the psionics will work in whatever way the author/designer wants them to.
In most books, psionic 'magic' comes from within a person. Only in rare instances does it's use hurt them in some way (such as the flawed psi experiments in Firestarter), but it does tire them, depending on the ability.
The Valdemar series uses both psi and magic in that world. Heralds are all psi users. They can mostly use their ability at will and without a lot of effort once they've been trained. The 'brake' on their power is that they usually only have one power and can never learn others. The mages in that world usually pull energy from the surrounding world or from ley lines and nodes; they do get tired and also sometimes have to wait for the surrounding energy to replenish itself.
In Darkover, most of their psi is communal. The 'brake' on their power is that most of it is done with a number of others to multiply their ability; a circle of psionics can change the weather, pull elementally pure copper from the earth, and lots more stuff. Individually? They're mainly limited to telepathy and ESP. Also here and in the Witch World series, psi is originally thought to be linked to gender: only women can be psi (in both series this is later disproven but gene-linked traits could certainly provide a 'brake').
Pretty much every author and designer puts in restrictions on any 'special power' to keep that character from being a nightmare to plot for,