I have 2 Coons. A 12 lb girl and an 18 lb boy. Both need to get more muscle and less 'belly-bag'. For several years I had 4. I am very familiar with rat-sized hairballs. If you can do it, going once a week or 2 on a day-long or half-day fast seems to 'bring them up' easier. I don't leave food out for mine all the time. They're fed 2x a day.
Cats are true carnivores. They have a short digestive tract. They can certainly injest vegetable matter, but can't really extract nutrition from most of it (it's not in the cat long enough). They do need roughage. Wild felines get nutritional value from partially digested stomach contents of the rodents they caught (sorry, might seem gross but true). Cats can't synthesize the amino acid taurine and will go blind if fed a totally vegetarian diet.
I don't know whether it was an old wive's tale, but I was told as a kid that cats and dogs eat grass instinctively, and that it helps clean their digestive tracts of worms. So, either it's a natural emetic (makes ya throw up) for a sick animal or a vegetable colon cleanser...your choice.