1. Functionality. Yes, really! Much to my surprise, the psionics rules given in the PHB and DMG are fairly straightforward and functional. They are, for all intents and purposes, a standard spell point magic system, albeit with more up-front random factors than are usually seen in the skill-based RPGs that tend to implement their magic type abilities this way. You have your various powers, a pool of points that fuel them, some guidelines for how fast spent points regenerate, and so forth. Psionic combat is oddly light on dice rolling for AD&D, and consists primarily of cross referencing various attack and defense types on a chart and applying the results. I'm genuinely surprised how workable the mechanical implementation actually is for those so inclined.
2. Feel. The details of AD&D psionics may not be too crazy in a wider RPG context, but they're weird as hell for AD&D. Whatever else the psionics practitioner might be, they're not just another core class using a cosmetically reskinned version of the base magic rules. They're...Something Else...Something Strange. That's honestly quite cool if you ask me. Beyond that, they're just such a full-flavor AD&Dism, tied to iconic monsters like the Mind Flayer and Githyanki/Githzerai. There's a mindset that says, "If you're gonna do something, do it with no all gusto and no apologies." That's AD&D with psionics, alright.
1. Situationality. By the book, psionics are rare. Really rare. A complete beast of a hypothetical PC with 18s in intelligence, wisdom, and charisma maxes out at a one-time 10% chance to possess psionics at character creation. 3% - 5% is far more realistic. As a DM, the prospect of learning an entire elaborate sub-system that might (might!) be available to 5% of characters can obviously smack of wasted effort.
2. Character balancing. Equally common and obvious are concerns about psionic characters potentially unbalancing the game. Thankfully, I do think they're overstated. Yes, psionics are "free" for the characters lucky enough to qualify for them. As anyone who's seen the film Scanners knows, however, mental combat between psionics is horrifically deadly. Furthermore, the DMG specifies an increased chance for random psionic monster encounters whenever psionic powers are employed by the party. A true risk/reward dynamic is thus present. Psionics make their wielders stronger than their mundane counterparts in some respects and more vulnerable in others, and players who know the odds may well prefer to go without.
3. The Decker Problem. Psionic combat really is its own thing. When two psychic figures are going mind-to-mind, they each take their actions on a per segment basis. In other words, ten individual exchanges per round! The remainder of the game basically pauses while they hash it out, and the rest of the table...well, they can cheer their buddy on, maybe?
The decision of whether or not to include old school psionics ultimately comes down to whether the individual DM feels that the sheer weird, wild tone of PCs lashing their Ego Whips against an intellect devourer's Thought Shield is worth learning an entire new "magic" system that probably won't see use often, but has the very real potential to hog the spotlight whenever it does come to the fore in combat. Personally, I'm leaning toward doing it in my next game, just for the freaky flavor of it and to actually get some solid use out of all those wacky monsters for a change.