It's not about saving a few bucks on a door. It's about discouraging you and your friends from sharing a single room. Hotel sees the money they're leaving on the table and will trade you for it for the low price of watching your buddies do their business.
In what way would it discourage you and your friend(s) from booking a standard twin room, if they don't tell you there's no bathroom door?
Dr. Strangelove: Of course, the whole point of a Doomsday Machine is lost, if you *keep* it a *secret*! Why didn't you tell the world, eh?
Here are the options:1. You offer double, twin and single rooms. Friends book twin rooms.
2. You offer only double and single rooms, in the hope that non-romantically engaged pairs of people will book two single rooms. Friends book some other hotel's twin rooms.
3. You offer double, twin and single rooms and you tell people before booking there's no toilet door. Friends book some other hotel's twin rooms.
4. You offer double, twin and single rooms but surprise! there are no toilet doors. Friends who've booked a twin room either demand a cancellation immediately upon seeing the room, demand a room with a toilet door, or they demand you offer some kind of ersatz privacy screen, and no matter what you do they're going to rain fury on every review site they can think of, tanking your reputation.
In which of these situations does the hotel get extra money?