There's definitely a demand for the work. In my world, there was no barrier to entry.
Getting paid for that work can be another matter. I can't remember the rule and who made it, but I remember our non-profit wasn't allowed to do the thing that worked best for all of us -pay the writer a percentage of each grant he brought in. Without the grants, we didn't have extra money around to pay him. Without being able to pay him, we didn't have him around to write the proposals.
I did a lot of grant writing -much of it successful- but had to be unpaid or paid out of the general budget (which had no money).
A friend had a full-time job writing grants for a very serious, life-or-death issue. After six months, still no results. She really took this to heart and it made her super depressed. She quit. It's very likely she would have seen a grant soonish -perhaps even on the proposals she wrote in the first weeks- but it can take time, and lots of nos can deal a blow.
Often an org's executive director or similar management level staff person will do it as part of their overall job, so they have other duties and successes to balance it out.
So, there is demand for good grant writers, but talk to the organizations you'd want to write for to see how they work out pay for that. And consider how you would keep your spirits up if more than one proposal were rejected, especially over super stupid reasons, local politics, competition, straight up lying by other applicants, etc. i.e., Determine how thick your skin is.
If you can do it as a gift to your favourite orgs, that's huge! A way you can direct big money to the org, without breaking your own bank account.