This isn't correct, most personal injury lawyers don't charge you directly. They take a percentage of the settlement or victory. There's way more money to be made with the "no fee" model than charging hourly in these instances.
I literally just said that they make their money on fees from the outcome of the cases. That is how basically every personal injury case works. If they don't think the case will win, they don't take it. Personal injury/tort lawyers do not charge clients in the same way as other types of law. They especially don't do that because a) they'd make less money and b) they are often times dealing with people that couldn't afford hourly rates up front especially as a case becomes more complicated.