I want two things: I want Psionics to be different from magic and I want Psionics to be just as simple as the rest of 5e. In my opinion, spending points would be a clunky and inelegant choice.
If it were me, I'd create something similar to WoD's powers: every Psionic power would have several levels, and as you progress, you'd gain more and more options. A seventh-level Psion could have, say, Telepathy 4, Telekinetics 2 and Clairsentience 1.
This has potential...I'm trying to see how it might work...it feels like it is right at the tip of my brain but I'm not foreseeing how it might play out or possible over-poweredness or abuse...
Something like, instead of how spells are divided into "power levels" with various slots of various levels gained at different levels of experience...
Psychics could have....no power points....no "slots"...but the powers they could take dependant on level of experience instead? Like...you take your discipline/focus/whatever you call them: Telepathy Telekinesis or Clairsentience...Then, what powers you have access to are "opened" as your mind and power level "expands" [by gaining levels sof XP]...
So the Telepathy powers might list "Detect Thoughts" and a "Daze" effect at first level powers. "Message/Send Thoughts" and "[Telepathic] Paralysis/Hold Person" under third level powers. "Psychic Blast" and "[Telepathic] Invisibility" at fifth.
Instead of Psychic Powers being listed as "1st level, 2nd level, 3rd level...", as spells, they get listed as "1st level, 3rd level, 5th level" so it is really as easy as when your PC is a given level they gain access to powers of that level or lower.' i.e. the Psychic Powers list, instead of listing 1st, 2nd, 3rd, 4th, etc... level effects, only lists the level at which they become available: 1st, 3rd, 5th, etc... (to keep them in line with odd level "bump to new spell level" of spell casting classes).
My question then becomes, how do you limit the use of powers? What is keeping the Psychic PC from just
Detecting Thoughts every round all day? They're never surprised and always know just how many people are around the corner/behind the door...and what they're planning. They can just
Psychic Blast their way through every encounter, no matter how many there are a day or how many HD worth of creatures you're facing. Who needs a stinking mage? Or rogue/ranger with a bow or frontline fighters? Every adversary is unconscious/mind scrambled before they ever hit the front line.
That seems terribly OPed when compared to other classes. So, I do feel some way of tracking/limiting power use all day is necessary. One of the tropes of the psychic is there are times their powers falter or they become too mentally exhausted or "tapped" of power or they are limited to "smaller/weaker" powers until some recovery time.
The historic/default is to just say "Power Points". But...there is certainly another way floating around in here someplace...Is "level +Cha. mod. times per day" or "per long rest" too
underpowered? Cha. [or Wis. or Int.]
score times per day?...or per short/long rest? Is that too divergent from how other class powers are monitored?
Like I said...there's a "non-PP" option (more than one, I'm sure, depending on the flavor and preferences from table to table) out there someplace...it's just a matter of is it "easier/simple enough"? Is it elegant/elegant enough? I can't say, unilaterally, of course. But I feel like there's a way...in there somewhere.