Interestingly look no further than Star Trek the Cage and Plato's Stepchildren for the power Psi's can abuse on mundanes.
The original inspiration for Psionics in Traveller (late 1970's) was probably the Force in Star Wars (MM stated that his primary inspirations were 1950's Sci-Fi and Star Wars).
Psionics also came from AD&D and D&D which Marc played extensively combined with the general interest in ESP that was around in the late 1970s (this was the time of Uri Geller and lots of pseudoscience).
The fascination for the paranormal, ESP, etc. arose in the late-Fifties/early Sixties, but reached a crescendo in the late Sixties and carried all through the Seventies as an outgrowth of the Counterculture Movement with its 'out of the box', Non-Western Cultural influences, alternative medicine (acupuncture, yoga), Transcendental Meditation, Eastern Philosophy/Spirituality (Daoism, Yi Jing, Sufism, Buddhism), Occult (Tarot cards), Xenozoology (Bigfoot, Loch Ness Monster), etc. I remember that time very lucidly...
...You would think with their Psi powers they could have easily picked up any technological information they wanted from the Imperium if not from other cultures.
...Plus their culture seems so oppressive like Sparta that I couldn't see how they could control so many different planets. I admit I haven't read everything about them yet.
Hmmm been contemplating what several people have written about the Zhodani on here. I guess I am looking at them from the perspective of the Fifth Frontier War boardgame.
As far as I can tell they have started every war. Not to mention in the Fifth they attacked much like the Japanese at Pearl Harbor only officially declaring war after the attack had begun. Seems they have become more and more paranoid though these wars and the encroachment of the Imperium on their star space. I can't see them not intelligence gathering (invading people's mind or mental rape as Far-Trader stated) it is a necessity of war. Especially by a culture suffering paranoia and fear of loss of autonomy. I get the idea that they think their backs are up against the wall.
I suppose their culture could be in a sort of crisis. The inner planets and culture much as Far-Trader and Aramis have described. their "ideal." And then the planets closer to the Imperium adapting to the Social Darwinism caused by frequent wars and overlapping spheres of influence.
One aspect of the OTU Imperium-Zhodani conflict that has bugged me over the years can best be summed up as a mini campaign. Allow your players to play a small group of 'Marine Force Recon' Zhodani types and turn them loose on the Imperium side of the border with a mission to raise economic and political havoc.