I stayed in an entire home (so not a private home but a home bought for investment). There was a cleaning fee. I left it like I would a hotel. That is towels on the bathroom floor, water glass left on the table. A chair moved from here to there. Rubbish in the kitchen bin. Not a mess, we tidied up and washed up, but certainly didn't clean up, except for the cereal which we spilled over the kitchen counter. There was a cleaning fee to cover these costs. I was given an awful and unjustifed review.
Anyway, the place would need to be cleaned before the next guest arrives (wouldn't it?). Just as in a hotel, even if a guest washes their coffee cups, the staff still needs to wash it again with the proper cleaning materials. Even if a pillow looks like it wasn't used, the pillow case is still changed. Even if a carpet looks clean, it will be vacuumed again to pick up the dust and the hidden toe nail clipping.
Now I am hosting - in my private home - and I charge a nominal cleaning fee for the cost of laundering the linen. I ask people to leave the kitchen as they found it and would presume they washed up as well as I would (I think you can probably tell by the type of guest you have that maybe you want to give the cutlery another clean), just as in some low star hotels or shared office space, you may want to rinse the glass before using it. I don't mind if they empty the kitchen bin, but don't expect it, nor that they mop the floor, vacuum the carpet, nor want them to mess with my vacuum. even if the kitchen counter was left tidy, it would still have a daily clean. So far I have been amazed at how clean my guests are and not really using the communal space as much as they could, not even eating the fruit I leave out. I am sure in time, something will be different. My offer is for a fully serviced place. It is reflected in the price. I am in the hospitality industry. I just think some people aren't cut out for hospitality and that is something you have to consider on airbnb, both when you are renting, and when you set out as a host. Like anything, you have to work hard to earn money. Now I understand there are other reasons to hosting, but you still have to take the rough with the smooth.
To sum up, if Sasha left baby sick on the sofa in my private home, I would hope he attempt a good job of cleaning up and told me straight away, and we would clean it up together while it was fresh. If he left the entire mess on a business rent, I would charge and mention they weren't the cleanest of house guests, but if he had attempted to clean it and left a stain, I would have to expect that as part of the business, it's part of accepting paying guests and allowing infants to stay.
In a hotel, we have had guests who spilled coffee on the sheets, apologise profusely and offer to pay for the linen; you don't mind cleaning up after them. Then you have others that spill water (or worse) on the mattress and don't tell you. Maybe hours later the room is cleaned and we have to go into over drive, changing the mattress, closing the room off, etc, etc. If we are told at the time, the systems can be in place immediately. Being told in advance helps so much, not least by taking the surprise away. Even leaving a soaking wet towel on a pillow means the pillow needs to be exchanged. For this reason my house rules ask that towels are left in the bathroom, not because I want the guest to tidy up, but it makes the whole cleaning process without extra surprises. I ask them to leave the duvet on the bed, it means the guest is less likely to leave any lost property behind; my school teacher always told us, 'a tidy desk is a tidy mind'.
If a baby was sick in a department store, you would hope the parents would tell a staff member and make an effort of cleaning up, but that the staff would say, 'don't worry, accidents happen, continue shopping and spending money', then close the area off and fetch a mop and bucket. That is the service industry.