Quick answer
Everyone queues at the palace. The verse says the thing they are queuing for is not finally in the building.
Read both lines
The NKJV footnotes "favor" as literally face, so the crowd is seeking the ruler's face, which was the idiom for access and attention. The picture is a corridor of petitioners, and the verse does not mock them. Seeking a ruler's help is a rational thing to do when a ruler decides things.
The second line relocates the outcome without telling anyone to stop petitioning. מִשְׁפַּט־אִישׁ, a man's justice, comes מֵיְהוָה, from the LORD, and the chapter has already said at 29:4 that a king establishes a land by justice and at 29:14 that judging the poor truthfully secures a throne. So rulers are genuinely involved in justice. What the verse denies is that they are its source, which is a comfort aimed precisely at whoever is at the back of the corridor.
Related: Proverbs 29:4 · Proverbs 29:14 · Proverbs 21:1 · Proverbs 16:33
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.