It’s not Mitches job to “offer counsel” here, He’s only supposed to “advise and consent” after the President makes his selection.
Without McConnell, you would have justice Garland instead of justice Gorsuch.
Further, senate majority leader McConnell has the power to bring confirmation to vote in senate or stop it as he did with Garland.
and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court,
Advise is a synonym for counsel.