I feel that psionics offers a non-Vancian system of spellcasting. Rather than magical blood, exhaustive study, or divine prayer, psionics represents strength of will and human potential.
I believe psionics would work best if most of the powers that simply duplicate wizard spells with more flexibility should be eliminated. (energy _, I'm looking at you!)
The point-based system is inherently more flexible and offers PC's more power than Vancian casting so I can understand why many players and GM's shy away from it as unfair. I do like the core concept, though.
What I would like to see is a system where, similar to Wild Talents in previous editions, a character could begin play with a few psionic talents. I would like to see a much shorter list of available powers, but have them retain the ability to be "pumped up" by greater point expenditure at high level. For example, a beginner at Telekinesis might be able to lift 1/4 their carry limit. As they level, my spending more points they might be able to use their full strength telekinetically, and at high level lift thousands of pounds.
Powers could even be purchased as Feats alongside a basic character class. Perhaps Psionic Aptitude could be a starting feat that gives a character a base Power Point pool (based on highest of Int or Wis.) Other feats could grant Telekinesis, Telepathy, Clairvoyance, etc.
For full-on psionic characters, prestige classes could be available, requiring high mental ability scores and several power feats as prerequisites.
Thus, any player who really wanted psionics could take them alongside an existing class (at the cost of the all-important feat slots of course.) Those really itching to play psionic characters might want to start in a class with high Int or Wis req's such as skill rogue, monk, or wizard and then gradually abandon their original training in favor of developing their inner powers along a prestige class path.
I think psionic classes are overpowered and the entire alternate casting rules steamroll over existing magical classes. Retaining the flavor and flexibility but making it run alongside normal classes, as it did in classic editions, would be the ideal solution for me.