This is analogous to saying "one of the absolutely critical considerations for banks undertaking mortgage lending is that they believe each loan is likely to be paid back. I fail to see why an outsider would embrace more risk than such banks."
But that is precisely what happened leading up to the 2008 financial crisis. And it happened because of outside financing. When banks were risking their own money, they maintained careful underwriting standards. When banks were risking someone else's money--and reaping fees instead--they relaxed their underwriting standards to increase volume.
A law firm undertaking a contingency case better be damn sure they are likely to win, because they are risking their own capital. A law firm with outside financing will get paid whether or not they lose.