To largely agree with what other people have mentioned before, I think that the rules for psi should be kept. Excising them would be no different from not including rules for fire or other phenomena; it would just be unrealistic for a "normal" setting to not include things that exist.
As an aside, it is honestly kind of remarkable that CT had psi rules at all. I do not think that many people have talked about it over the years, but it is pretty clear that Marc had some pretty strong anti-psi views in the past, although they appear to have lightened in recent years (I remember that the book with the wafer jack agent had pre-existent souls and ghosts). Marc repeatedly downplayed psi in the 3I in lots of little ways. Psi being criminalized in the Imperium (kind of an X-Men-esque trope, but really makes about as much sense as making using your eyes illegal), psi scores decreasing with age unless trained (which was not even empirically supported by scientific research at the time when Classic Traveller was published; granted that was also complicated by the fact that it was intended to counterbalance the advantages in skills that older characters had), that one passage that went over the history of psi research in known space that claimed that parapsychology on Earth was not true psi research (do not know if it is related, but Mongoose also seems insistent on using the term "psionicology" which is more of a pure SF term). I also vaguely recall hearing Marc express the belief that paranormal phenomena cannot be understood scientifically on a science-fiction podcast that he was invited to, but as I do not really want to focus on that as I cannot remember the name of the podcast. I do not mean to be too harsh to Marc and again I think his views have softened over years. Weirdly enough for a brief time it seemed like Mongoose was expanding the rules for psi a bit more in Mongoose Traveller 1e (the Society for Psychical Research was founded in Britain, and it seems like some of the academic attitudes towards psi there have affected science-fiction media over there). Do not know what they have planned for 2e, although I do know that they have mentioned that they plan on publishing another Psion book.
It is kind of a miracle that psi got into the LBBs at all, and have stayed a part of the core rules for so long. Part of it is probably due to the Zhodani and such, of course, but it is still pretty remarkable that pretty much every edition of Traveller has had playable rules for psi powers, even if there are also the warning signs of "this is illegal according to the default setting," and such that make it seem more optional. A lot of games would have just gotten rid of the rules and have it be an NPC thing or something. In that regard, I am grateful that the psi mechanics have been retained for so long.
