I dunno about the signature requirement. Most of the obama birth lawsuits were thrown out for standing from what I recall.
You and I cannot challenge their qualifications unless we are running for the same office.
Probably a good thing overall as it would allow activists to clog the courts. A bad thing in some cases.
In order to get on the ballot, a person has to meet several requirements. One of these, in some states, is gathering signatures of supporters. Another, in all states, is to be eligible for the office sought.
What is inconsistent on the part of the courts is that they are willing to entertain a remedy for one criteria (signatures), but not another (qualification to hold office). The "standing" rationale says that no voter is affected if a name wrongly appears. That answer doesn't distinguish WHY the name wrongly appears, just that ineligible names on the ballot are a harm with no right to a remedy, unless you are an opponent on the ballot; or that the venue to remedy the harm is electors and Congress, not the courts.