>It's something that wouldn't happen without the money

People never have sex, hook up or send nude pics of themselves without exchanging money?

You're conflating what sex workers do with what people who feel lust and excitement and decide to get intimate do.

You should spend some time with sex workers. Pretty much the first lesson in this line of work is that you act well and submit to the whims and wishes of your clients, and the second lesson is to put some hard limits on what you'll do or you'll be abused.

It's generally an act, one person faking attraction or friendship or whatever and another person paying for it. Sometimes sex workers get to know clients personally, but outside porn where the 'client', i.e. the producer or whoever is paying, isn't the one you're fucking I've never heard about a sex worker initiating a non-paying relationship with a client.

To answer your actual question, no, this is not a common type of behaviour.