Based on Theravada, which is what I'm most familiar with, vegetarianism is not essential for any meditation that I know of. Even so, I've chosen to be a vegetarian. As I understand it, the Mahayana tradition tends to strongly encourage vegetarianism, but even then I'm not certain if they do it specifically to aid meditation practice.
As to it being profitable, it depends on what effects adopting vegetarianism has on that person's state of mind. If being a vegetarian helps your compassion towards beings, then you might consider it profitable. For some people, choosing vegetarianism might result in no improved state of mind, in which case it doesn't matter.
This also answers your third question as to why a lot of people become vegetarian after they start their path. They might have noticed that becoming a vegetarian, for them, improves their personal state of mind. Of course this won't be the only reason, but for some it might be.
Try it, and see what works for you.