It might help to keep an eye on what distinguishes "magic" from "religion" from "science."
When the distribution of outcomes is fairly-well understood, activities take on a Scientific character. If you do X and Y under condition Z then you get beer 90% of the time (and an inedible mess the other 10%), that's basically a Scientific undertaking. Advanced Science involves abstracting away the essential elements of relationships into theories to apply them in new situations.
When the distribution of outcomes is mysterious, activities take on a Magical character. If you do A under condition B and C happens, then the presence of A and B causes C until proven otherwise, especially if controlled experimentation is not feasible. In everyday life, this is known as falling back on heuristics. Apparent contradictions call for rationalizing B, and can get quite complicated like a Scientific theory. A lot of ritual can be explained as a way of getting the practitioner into a frame of mind that is more likely to lead to success.
When the distribution of outcomes is too important to leave to debate, activities take on a Religious character. Whereas Magic is often utilitarian and on a personal scale (improving one's chances in the hunt, or healing a sick relative), Religion deals with social issues that are Too Big To Fail. Religion is preventing plagues, regulating the seasons, and tramsitting culture to the next generation. By its nature, Religion tends to scope-creep into prescribing about every facet of public life... and the explanations are typically expected to apply in private as well. Magic tends to be occult (private or small-group hoarding of esoteric knowledge) while Religion tends to be overt.
Note that Religious figures can resort to what I'm calling Magic, though they would not call it that. In the real world, Baptism and Matrimony would be Religious rituals, while Exorcism would be a Magical rite.
An example crossing all three categories might help. Hunting fish in a lagoon is pretty safe, and eventually people will figure out what works and what doesn't. This will be a Scientific exercise with a skill that is handed down from father-to-son or mother-to-daughter. Hunting sharks on the open ocean invites lots of potential for disaster, most of which are dimly understood. This will be a Magical exercise with plenty of ritual and symbolism to recall past successful hunts. Hunting heretics within the community carries risks too great to leave to fallible mortals. This will be a Religious exercise with unassailable justification, and probably a lot of extrapolation from failure-to-observe-a-specific-norm into this-is-a-bad-person.
"Wild magic" is an attempt to shoehorn Magic's mysterious outcomes into a game full of inherently Scientific rules.
One alternative is the one Toady mentioned, which is to give the magical ability its own personality... and make outcomes depend on the state of the relationship in that instant. This isn't too far off from the Avatar concept in Mage: The Ascension, except that that game relies far more on roleplaying than dice.
Another alternative is to simulate the development of Magic during pre-history (myth generation) and history (worldgen), perhaps borrowing some of the elements of art/dance generation to lessen the level of detail necessary in the simulation. Basically, a set of associations gets built up to form a Magical framework. The complex web of causation allows for a healthy chance of failure... and a non-trivial chance of getting a wholly unexpected result.
So, instead of trying to build a better Wild Magic Table, try to find a mechanism that does a satisfactory job of accomplishing the real goal: mysterious outcomes.
Edit: Grammar