Sure, do whatever you want. But girls only ask for this stuff because guys like you are willing to give it. In every part of the world I've been to where sex work is more mainstream (UK, HK, Japan, etc), nobody will ever ask for this stuff from a client, but they WILL go head over heels to provide you verification that the girl you are paying for is the girl in the pictures. This is how it is supposed to work.
Clients are the customers and are paying the money. There are other ways to ensure safety rather than making somebody send you sensitive personal information. Beyond that, sending a "blacked out" ID provides literally no value, as they can't run a LE or criminal history check on you on that basis. All you're doing in that case is sending a criminal selfies.
The girl is not going to trust you with a photo of her ID, her legal name, or her LinkedIn profile. Why would you trust her with yours? Would you send a verification photo to a drug dealer? No? Then why would you send it to a prostitute? Would you believe a drug dealer if he said he deleted your photos? No? So, why do you believe a prostitute?