£75 is a lot for adding even an adult to the room, never mind a child - was the booking changing you automatically to a family room or something and you were accidentally booking for 2 adults and one child? The booking systems online can be a bit weird at times, I use one at work but have been tripped up by 3rd party ones or other places. (I don't know about air BnB though)
I work in a hotel and the we charge extra for each additional guest, and half of that for a child and nothing for an infant (under 2) and if one person is booked and two arrive, we charge for the second guest or refuse check in. And we also ask extra guests to leave if it takes us over occupancy for the room or the hotel and we find them and they aren't booked in and haven't paid and the original guest too if they refuse. We charge extra for the towels and things in the room used, and for the additional electricity and hot water that the second person uses. Though we don't charge anywhere near £75 even for an extra adult!
We also have to have a current guest list, and the name of each person in the room. And part of that reason is in the event of an evacuation.
No, the fire service aren't going to be going off a list when looking for people, people go out etc and may not be there at the time, however we use the list to account for who we have, and then attempt contact with those who are checked in and on the list, but not accounted for, to ensure that they aren't still in the building, as hotel staff we'd do this, the fire service will be checking each room/area for anyone trapped regardless of what I have on my evacuation list, but we would endeavour to make sure everyone on the list is accounted for one way or the other at some point following the initial evacuation and accounting for people, and also, as horrible as this is, if someone doesn't make it out, are unaccounted for and a body is found, it's a starting point towards identification of that person.
It's just good practice to have a current and up to date list of who's staying in your hotel. I can only imagine the uproar if someone were unaccounted for after a fire and the hotel didn't even know they were staying, because they only had one person on the room and hadn't bothered to update the booking when 2 people arrived.
It also invalidates our insurance as other pps have said.
I agree that the charge is a lot, but it doesn't justify deliberate deception, you are not happy with the price and I totally get that, it's an awful lot for a small child and the other details about adding an adult for the same price don't make sense, however you're not being forced to book it, those are the terms they offer and if you're not willing to accept them then you don't book and look for somewhere that the terms are acceptable to you.
As a pp said, it's not a public service, and if they're charging such prices and people find alternatives that suits them better, then they lose the business and will need to look at why. But that's for the person running the business to decide, not the customer.
The business offers it's service, terms and price and the customer is at liberty to accept or decline, they don't change the terms of service by demand (and threats of TA reviews 🙄) or deception because what they want isn't offered - I agree with others that this is entitled behaviour, although more and more common unfortunately. Or book, get what they booked and then complain about it because it wasn't what they expected in their head - even when the terms of booking and the information is clearly laid out and provided.
It's good to see you got sorted though, most booking sites are generic, where as ringing up direct usually gets a better result and you can get extra beds or bedding etc and then both you and the hotel know where you're at.
Enjoy your trip - York Christmas markets are lovely!