Why should you take NSAIDs with food?

I know that part of the mechanism of NSAIDs causes a reduction in protective stomach lining, which can lead to stomach upset. But this is due to the mechanism of the drug and not the actual chemical components of the drug, so i don't see how taking it with food can help with the stomach pain since it won't stop the mechanism. I've tried to think of explanations for this and i thought maybe taking food will soothe the pain? But if this is the case, then why is there no instructions to take food with injectable NSAIDs (ketorolac)? It too will reduce the stomach lining, therefore causing stomach upset. Absorption for oral NSAIDs is pretty quick, while injectable is immediate. Shouldn't the onset of stomach pain be similar as well?