Question

Why is it in the president best interest to nominate federal judges favored by most senators

Answer 1

Even though the senators do not possess the final say in choosing who's gonna be the federal judges, they could still make some efforts to put the process on hold because the senators have the obligation to advise the president regarding this matter. So, to make the selection process faster, the president could nominate the one that favored by most senators so he could move on in handling other programs.