This question depends largely on the game format, stakes being played, and player goals. It’s easier to bankroll yourself for cash games as they have less swings than tournaments. Likewise, if you are happy with the stakes you are playing and have no desire to move up, it will be easier to play with your own money. On the other hand, if you play tournaments with very large field sizes, varying buy-ins, and/or want to move up in stakes then playing with your own money will be possible but more difficult.
What we know about here at Pocarr are multi-table tournaments (MTT’s). Most of our players have a desire to improve and move up in stakes. For this reason many are giving up a percentage of their profits not just because they need the financial backing, but because they want the coaching we provide. Another large section of our players simply want their own money to be working for them in other ways. They may be more comfortable having their money in real estate, or stocks, and prefer to leave the poker swings to us. Lastly, there are many players who do need the financial staking and do not have the means to play the games they want to play without financial assistance.
In the MTT community it is very common for professional poker players to be staked. In cash games it is far less common and it seems most are using their own money.