20% of the population are nobles or Intendants. Some of those are telepaths. And some of those telepaths are not capable of effectively mind reading, because nothing guarantees a Noble has a decent PSI strength or sufficient skill to reliably use the more complicated techniques.
But, as I mentioned before, Traveller has done the barest of minimums on defining psionics and only slightly more than that on how it actually works in the Consulate, so you can envision it however you want, really.
My point is that specifically looking for the extremely rare spy with this level of full court press is a pretty extreme level of paranoia that I don't think suits the Zhodani mindset. Perhaps you can practice that level of paranoid suspicion without infecting others, but I personally find it rather unlikely. Not to mention, if you are dedicating that much of your limited telepathic resources to catching spies, they aren't doing a lot else.
Since the psionics rules essentially say that you can have Telepathy if you want it, you can be sure that in every group of 5 trained Zhodani psions at least three of them will have the talent... in addition to any others they may have.
As for the full KGB paranoia treatment, I want to remind everyone that the Zhodani fear the Imperium as much as the Imperium fears them... Those Zhodani trained in deception are fully aware that the Imperials are orders of magnitude better at it than they are, just as the Imperium fears Zhodani psionics. And remember that there's only so much ability at deception and dissimulation that a Zhodani, ANY Zhodani, can get away with before their mental health is compromised and they get reeducated. This means that intelligence executives... the people ultimately responsible for acting on the intelligence gathered... are only so skilled at the craft. Their Imperial counterparts are more skilled at it but, because the Imperial intelligence services are part of the military services, they have a harder time getting their superiors to take heed of the warnings.
Consider: there are several service paths that almost prevent a serving officer from getting those choice commands that lead to flag rank. Logistics, civil affairs, technical engineering, and intelligence are NOT the career pathways to become a Sector Admiral. There are a lot of people in all those fields who have 'been judged and found wanting' insofar as command is concerned. For example, do you know what the US Air Force calls the missile combat crews [that is to say, the guys with the keys to the nuclear safes]? 'Washouts', that's what. Despite decades of work by USAF personnel and generals, the missile watch officers are guys who'd rather be flying. And in the Chair-Force, you're either a pilot or a third class citizen hoping to be promoted to second class citizen some day if you work ever so hard at it. To put point on it, there has NEVER been a Chief of Staff USAF that wasn't a pilot. In the same vein, skilled Army J-2's don't get command of divisions and, in Traveller, able Naval Intelligence specialists don't get command of
Tigresses. Most of these officers top out at Colonel /Captain and are retired.
And it is these 'washouts', each of whom knows that they're looking at Life After The Uniform a lot sooner than their cruiser commanding Academy classmates, who have to look at the raw intelligence, come to conclusions, and get the Admiralty to understand the intel, what it means, and what can be done about it.
My entire point in this Wall of Text is that BOTH the Imperial and Consulate leadership have biases that can and do cripple their intelligence operations. The trick is to find the chink in the armor, but each society puts obstacles in the way that job a lot harder than it has to be.