On August 15, the Texas Libertarian Party filed this brief in In re Self, 22-0658. This is the case over whether Libertarian nominees who didn’t pay the filing fee should be on the November 2022 ballot. The issue turns on statutory interpretation, which is quite complicated in Texas election law.
Censorship is always an arbitrary to keep an incumbent elite in power. There is no “rational basis” for ballot access censorship.
Prior to adoption of the Australian ballot it was possible to elect someone who was ineligible for the office. This would effectively void the election. Once the government began printing ballots it became possible to check eligibility before the election. If John Smith is on a ballot, an ordinary voter will/might assume that Smith is eligible. If John Smith is ineligible to hold office, he can be removed from the ballot, reducing the risk of election of an ineligible.
It might not be discovered until after a nomination is made that it is discovered that a nominee is not eligible, For example, the nominee for US senator might be 28 YO. He might have confused the qualification for senator with that for representative, or he might have perjured his application.
Eligibility may change during a campaign. A candidate for the state legisture might be convicted of a felony or move from his district.
A party officer makes the declaration of ineligility, and the party may then make a replacement nomination.
The Republicans are claiming the Libertarian candidates are ineligible. If this were true it would be be a violation of the US and Texas constitutions by adding to the exclusive qualifications for various offices. See ‘US Term Limits.