First, the rules I was referring to on challenging candidates are set by state statutes, not by the courts.
But in general, the rules of standing come out of Madison's idea that the judiciary was to be the "least dangerous branch." The courts are the furthest from popular control of any of the three branches-- judges are appointed, and serve for life-- so they were never meant to be makers of public policy. Courts were designed to settle specific disputes between specific parties; they have the power to declare laws unconstitutional only if the issue comes up in the context of a concrete lawsuit between two adverse parties. (The Constitutional Convention considered, but rejected, a plan under which all new laws would first go before the Supreme Court to decide if they were constitutional.)
Accordingly, courts have held that, in essence, if everyone has standing, then no one has standing. This is not as paradoxical as it sounds; if an issue affects everyone, it should be resolved by the elected branches.
Historically, it has been conservative judges who have been the strongest defenders of tough standing rules, and liberal judges who most sought to bend them, because standing is what limits the power of judges to make policy against the wishes of the majority.
No one is asking them to make policy, although Lord knows they do that all the time. They are being asked to enforce the Constitution. Pretty simple really. If they won't do that, they are FReaking useless.
Not buying it. This is not a legal issue that requires any one citizen to receive redress. It by its very nature affects all citizens so indeed, all citizens have standing and any resulting remedy is applicable to all citizens. No conflict there. The elected branches are not disinterested parties in this case. They have a massive and self interested dog in this fight. The judiciary should be placing themselves squarely into the middle of this issue. That's what they were set up to do.