I think I preferred the Traveler approach to psoincs: they were very limited in scope, power, and availability, were vaguely known and could be dealt with to some degree by the non-psionics of the society in which they existed...What's your favorite/favored way of working with psionics/psychic powers?
...and, most importantly, they were in a science-fiction game, where they belonged.
That said, psoinics should probably be included as a module in an established setting, like Athas, where they serve an important function. While it might be OK to have full-on psionic classes, they definitely should leverage their multi-class or feat (or Background) sub-systems to allow for 'wild talents,' too.
Given the 5e disparate-mechanics mandate, psionic classes should work on some sort of 'power point' system that evokes the classic psionics (hopefully in a much less broken way), and makes them very distinct from casters.