Nominations of the justice is done by people who have been elected though. According to you, does that make them less legitimate that if they were directly elected?
Not OP, but yes, adding additional layers of indirection makes an election/nomination less representative of the will of the people and thus "less legitimate" if you think legitimacy is based on representing the will of the people.
Of course the bigger problem according to this perspective is that there are many more layers of indirection before it even comes to the point where "your" elected representative nominates a judge. Some of them are more prone to "shaping" than others (e.g. via gerrymandering, disenfrachisement, voter suppression in all its forms) but the goal is generally to generate "favorable" election results regardless of what the people currently want.
