I don't think psionics combine well with magic. I have no problem with either but I like to see them each in their own setting.
See, and for me a setting that does not include all three 'classic' power sources (arcane, divine, and psionic) is incomplete.
Note that the power sources don't have to go by those names, which is imho, often the 'real' reason why people feel, psionics have no place in a fantasy setting.
My personal understanding about these sources actually comes from the Rolemaster rpg:
- arcane == essence: drawing power from the environment, tapping residual magical energy
- psionic == mentalism: drawing power from within yourself
- divine == channeling: drawing power from magical beings (deities, fiends, spirits, etc.)
Going by these definitions some of the D&D classes actually resemble different power sources, e.g. sorcerers really should use the psionic power source and warlocks resemble divine casters more than arcane.
All of them are 'magic', what's different is where the energy's drawn from.
For me there's also a kind of hierarchy involved here:
The true masters of magical powers can draw power from pretty much everything (essence), but it's also the most difficult to learn, hence wizards who epitomize this approach, require a long and ardous education.
It's slightly easier to fuel spells by drawing on your own resources (mentalism), so this is something that talented individuals can do without requiring a lot of schooling.
Finally, divine magic doesn't really require education or talent: everyone can do it by dedicating themselves to higher beings and becoming vessels for their magical powers (channeling).
Now, mechanically, it's not strictly necessary to devise three different sets of rules, but they kind of lend themselves to different approaches:
E.g. it's easy to imagine that drawing power from the environment may take a longer time and/or is more formulaic but offers the advantage of being potentially the most powerful.
In D&D I see this represented by requiring memorization, studying and preparing spells and improving spells via metamagic feats. I also like the idea of spells that become more potent if you take more time to cast them.
I particulary liked the 2e Dark Sun defiling magic - that was exactly what I imagine would happen if spellcasters didn't consciously limit themselves or lose control over their magic.
If you're drawing power from within yourself, it's more flexible but might be mentally or even physically taxing.
In D&D this resembles spontaneous casting or spell / power point-based systems. I liked that in older editions, using psionics was very fast. Also, when psionics was introduced in 3e, it was the first system using swift and immediate actions.
Some psionic feats allow trading life-force for power by spending hit points or taking ability damage. That's also quite iconic.
Channeling magic could resemble both of the above, depending on the way the being drawn upon works its magic. So it might be fast and flexible but with little control over the actual effects or require elaborate rituals with clearly defined effects.
In earlier editions of D&D when praying for spells, it was possible you might not always be granted the spells you wanted and there was a mechanism for divine intervention.
Making the power sources feel different from each other could be as easy as introducing power-source specific feats modifying an identical basic mechanic.
Regarding skill-based spellcasting systems: Well, I don't know how the Star Wars force powers work, but I do know the fiasko that was 3Es Truenamer. Hence I have trouble imagining a functioning, balanced system based on skills.