The existence of a triple point is not a coincidence at all. It will be a necessary feature as soon as you have three different phases in your phase diagram that can all be reach from each other.
It's like when you have three countries that all share borders. By geometry alone there has to be a point were the borders intersect.
The position of the triple point, however, will of-course depend on the details of the substance at hand.
EDIT: Because thermodynamic phase diagrams can have critical points where phase boundaries terminate, the above rough explanation is not entirely true. One can think of situation where the third phase borders the critical region, as bellow:
However, I know myself of no such phase.
Apart from this I don't see how you can avoid the triple point. (I'm happy to be shown another (non-trivial) example where the triple point is avoided).
IN COMMENT: You may also be interested in looking at Gibbs' phase rule.