Quick answer
He is not killed by having no wants. He is killed by wanting things his hands will not go and get.
Read both lines
The verse locates the fatal thing in the desire rather than in the sloth. A man with no appetite would simply have less; this man wants, continuously, and the wanting has nowhere to go. Then the second line supplies the reason with a verb of refusal, the same verb the chapter used at verse 7 for the wicked who refuse to do justice. The word choice puts this squarely in the territory of will rather than capacity. It is the gap between appetite and hand that does the damage, and the next verse shows what the gap looks like from outside.
Related: Proverbs 21:26 · Proverbs 13:4 · Proverbs 19:24 · Proverbs 20:4
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.