I've only ever stayed at the Ambiance and Don/Elephant Plaza over the years and the guy has always been asked to leave his ID at the front desk.
Over the past few years I've just spent my holiday with one guy, rather than off a different guy every night. But even so, the Ambiance still asked for the ID card even though I was bringing the same guy back every night and he was friends with some of the staff there. At the Elephant Plaza, the guy I'm with is well known to the manager and staff and he spends a lot of time in the hotel with me, so they no longer keep his ID card at reception. However, they do have a photocopy of it under the counter.
I think the bar owners have a lot to answer for here. Surely,if as a business they are employing guys for us to take back to the hotel and are willing to take an off fee, then it's up the them to ensure that the guy has an ID. He could insist that the non-Thais bring their passports to the bar every night. No passport, no work for the night.
I got caught out a few times in the early days when the guys I offed didn't have ID cards and the hotel wouldn't let them in, even though they were clearly over 18. I'd just go back to the bar and ask for a refund of the off fee and look for someone else. After that, I got into the habit of asking the guys at the beginning whether or not they had an ID card and that solved the problem.