The purpose of no bathroom doors is to limit their use to single people or couples. They want business travelers to get a separate rooms or upgrade.

I can assure you not even single people nor couples want doorless bathrooms.

No, it is because doors take up a lot of space. A typical door is 3 feet wide, and requires 7-14 feet of empty space to operate [0]. You can't place any furniture, toiletries, or luggage racks in this space. For a typical hotel room of 300sq feet, this "dead space" represents 3-5% of the room. Removing the door allows hotels to decrease the size of each room, and fit more rooms on each floor, increasing profit.

This is why many newer hotels choose to sliding doors, which barely take up any space, or just remove doors entirely.

[0] For a door of r=3 feet, A door swings a minimum of 90 degrees, which takes 3.14 * 3*2 / 4 = 7.065 sq feet at a minimum to 14.1 sq feet to operate.

I'd imagine that most couples would still want to be able to close a door when they're on the toilet.

I'd rather sleep in a shared room at a hostel and use a toilet in a stall in a communal bathroom than in a hotel room without a proper door on the bathroom.

Whether the room has a door on the bathroom or not, business travellers should be getting separate rooms... Over dozens of trips, the only time I've ever shared was a two-bedroom apartment when I went with a colleague for a conference (one had an ensuite so we had separate bathrooms as well as separate bedrooms with doors).

I wouldn't be OK with going on trips (or sending people I manage on trips) where two people had to sleep in the same room, I wouldn't consider that acceptable...

Unlikely, given that you don't know it has no door until after you get there.

And also, when I travel with my kids, I still want to close the door.

I'm in a committed long term relationship. I absolutely do not want to shit in front of my partner (nor do they have any desire to watch).