Let's us dieting as an example. Verse 20-21 tells you to diet. Verse 19 tells you HOW to diet. We can be ambassadors for diets, telling everyone they need to diet, but without verse 19, we aren't telling them HOW to diet.
Not imputing their trespasses unto them, gives us our WAY to be reconciled to God and become ambassadors for Christ. Without verse 19, we are left with not knowing how to be reconciled to God. It's the GOOD NEWS that is left out. The NEWS that saves.
Actually, it doesn't. It defines, in part, what reconciliation is, not how to get it.
(Non-imputation of sins is the bare minimum; God seeks to completely remove our sins from us along with all of the damage they've caused. He doesn't stop at mere non-imputation.)