Why isn't "Elephants don't eat grass"? I understand the verb has not been conjugated to plural but it's far more natural sounding in English
So if this sentence had "haiñ" at the end, then it would be "the elephant is not eating grass"?
No. The हैं at the end of the sentence wouldn't make any difference to the overall meaning. In fact, I suggest you not to drop it as most Hindi speakers don't.
To say - The elephant is not eating grass - you would say,
हाथी घास नहीं खा रहा है।