CO skier
TUG Member
It works no differently than Airbnb or Vrbo. Guests don't get printed confirmations there other than what Airbnb or Vrbo shows them on their website. You are putting trust in the third party company to make sure things are right. And in the case of these two sites and Koala, the owner doesn't get paid until after checkin. Also realize, that most people don't print things out anymore and their target market is not necessarily your generation.
I get the sense it isn't any different than, say, Expedia. You get a confirmation from Expedia, but not from the hotel itself. In some cases, your name isn't even sent to the hotel until much later, because Expedia has a block of rooms to sell, and that block is theirs, so they don't need to. Most rank-and-file guests have no idea how complicated things are in the background, they just know that they have a "confirmation" from Expedia.
With age and 100s of thousands of miles of business travel, comes experience and wisdom. One of my last hotel bookings with Expedia was for a business conference about 15 years ago. I arrive at the downtown hotel, and they have no record of a reservation. I open by briefcase (I know, "my generation") and pull out the file folder with my printed confirmation. They still could not find my reservation, but it had enough information that I received a room for three days. Fortunately, it was early afternoon and there was a room available; maybe someone checking-in after 10 p.m. did not get a room when their reservation could not be found.
Just this last summer, I arrive at the Super 8 in Boise, ID. The 20-something clerk, who did not seem particularly motivated that day, could not find a reservation using my name, "Sorry, sir, there is no record of a reservation in your name" and that was the end of the conversation. I go out to the car, retrieve my laptop, and show the clerk the confirmation .pdf I saved, with my name on it, when I booked the room. Problem, reluctantly, solved with no apology. Kids these days ...
I have always, in 30 years of travel, received a confirmation with my name on it when I booked the reservation. Sometimes I call ahead to confirm a reservation or with a room request. They have my name on the reservation then.
Maybe it is because there are no charges for guest certificates at the places I stay.