The search result that gave you that advice is wrong. A fluent speaker would normally say "good for health". I would use "good for the health" if health was further qualified. For example, it is okay to say "That would be good for the health of everyone."
One common reason for using "the" with health is when health is being used as a substantive adjective. Examples: The health care system, the health initiative, the health network. In those cases, the definite article really pertains to the noun that health is modifying.
The definite article is also sometimes used when health is the subject of a sentence and is further qualified. Examples: The health of the nation, the overall health of cancer survivors.
- For Teachers