The AZB Money Leaderboard shows there are barely two dozen players who can claim to 'make a living' from pool tournament winnings. Over halfway through the year Number 24 has won just $33,062. If the player keeps to that average winnings he or she would gross about $57,000 for the year. But that is the gross income, not the net. Real expenses draw this amount way down - things like entry fees, transportation, meals, and hotels. Another expense is practice time, which will either be the amortized cost of a home pro-quality 9' table, or several hours table time at a pool hall every week. If a real pro lives in the US they have to account to the IRS, and possibly pay SSDI tax. AZ's own reporting of winnings makes a case that there isn't enough money in 'pro' pool for more than a few to make a living on tournament winnings.
Of course a few players will get comp time on almost any house table anywhere. Another few will have sponsor's logos on their apparel, which will likely net them as much or more than their tournament winnings. Some will get sponsors to buy equipment - cues, cases, gloves, gadgets, etc., and maybe even underwrite tournament expenses.
There will always be the winnings from gambling, often using backer's money. But one does not need to play pool well to gamble on it.
Pool is hardly a sport, yet. Calling it a hobby with tournaments might be more accurate.