So who WOULD have standing in such a case?
The other candidates can meet the criteria for Article III standing because they can demonstrate DIRECT injury-in-fact from an ineligible opponent: Trump and Kaisch would always have standing to bring an eligibility lawsuit. They could even be lead plaintiffs with other citizens (registered Republican primary voters).
As Nero Germanicus said, most people believe that another presidential candidate would have standing. Others believe that the courts consider these cases to be political questions and thus won't hear them.
I read some of Judge Pellegrini's opinion in Elliott v. Cruz. He made some good points about the political question doctrine not being applicable.