My husband shared rooms with our daughters when they were teens, and so did a lot of other dads that we knew.
Our daughters were (and still are) figure skaters, and went to many competitions over the years, all the way through their teenaged and college years. If I had to work and couldn't go to the competition, my husband would go, and the girls (or just one girl, depending on who was competing) would stay with him in the hotel room.
There were a lot of daddies who stayed with their daughters at these competitions. Usually parents travel together, but there are lots of situations like ours, where Mom either had to work, had younger siblings and babies at home to care for, or there was a divorce or separation.
Also, when our daughters were doing college visits, I often had to work, and so their daddy would drive them to the school (often far away) and they would share a hotel room.
Two years ago, my husband drove my daughter cross-country out to California (grad school) to move her in--I was not able to get the two weeks off work. She was 25 at the time. They made a real Western vacation out of it, stopping at the tourist sites (e.g., Grand Canyon). And yes, they shared hotel rooms.
Yes, there are privacy issues. They are solved by taking turns in the bathroom and shower, and keeping the door shut.
There was never any bed-sharing, not even between me and the girls when we travelled. Our daughters would sometimes share one bed while my husband and I shared the other bed.
Interestingly, in the skating novel that I just published a few weeks ago, the teenager is on a vacation with her parents, and they are all sharing a hotel room because they don't have the money for separate rooms. I never even thought of the possibility that someone would possibly see privacy problems with this. The editor didn't ask for any revisions of this, either. I realize that it's not daddy and daughter, so perhaps that's why it wasn't questioned by the editor.
At any rate, unless rooms are adjoining with connecting doors, or unless a suite is booked, I think that teenagers should not be in a hotel or motel room alone. If there are several other teens in the room, that's OK--safety issues. But I would not put a lone teenager, girl or boy, in a room by themselves. Too much of a target for creeps.