I’m not sure what you could mean here. What qualifies someone to hold any political office is their conduct and their rulings and how those are interpreted is by what the people believe is fair.
A judgeship is not a “political office.” Yes yes yes, I know - I hear you clicking the “reply” button, but it’s not supposed to be. And by making them directly voted on they they definitely will be.
I’m going to preface this with “none of these problems are solved by either options but some things are better in some situations than in others.” There is no silver bullet.
But - I want you to imagine a scenario: A judge wants to be on the supreme court.
Scenario 1: Big Evil Co. starts up a PAC that spends billions on getting that judge elected and they win. Big Evil Co. has business before the court and threatens to dissolve the PAC when the judge comes up for election again. Maybe PACs are illegal in Mexico - I don’t know, but they can find some way to fund campaigns since they’re often expensive ordeals.
Scenario 2: An elected official who was chosen by the people (sometimes the good people, sometimes “those other guys”) nominates somebody for office. They are chosen by other elected officials. Now when Big Evil Co. comes before the court they don’t have many options. They can bribe or give gifts. But they can’t really effect whether that judge remains on the bench. And such actions are often deeply looked down upon or outright illegal.