@Ian-And-Helen0 Hosts can choose whether to offer breakfast or not. Do what is most convenient for you and your routine, facilities and inclinations. The breakfast you offer sounds just great, but you aren't obliged to offer it unless there is nowhere for guests to eat out and if you don't want them cooking in your kitchen.
Where I live there isn't anywhere to go out to get breakfast and I don't want to have to clear up after guests in my kitchen, so I provide it. I make a full cooked breakfast, because that is traditional here. I actually find it easier than the self-service option with pastries, yoghurt and fruit as I have a long way to go to shop and can't always guarantee to have these items fresh, whereas you can freeze most of a cooked breakfast.
If I go abroad and book a hotel room or an Airbnb Private Room in a city, I enjoy going out for a local breakfast. If I go away for a few nights with my husband to a rural Airbnb here in Scotland we will always choose one with the luxury of a full cooked breakfast. Many Airbnb's here don't offer a hot breakfast.
B&B stands for Bed and Breakfast. Airbnb doesn't mean Bed and Breakfast but just hints at something similar and at the airbed origins. Hosts have the option whether or not to tick the Breakfast box in Amenities, and guests have the option of filtering for breakfast, it isn't compulsory.
From reading posts here, I would say that most city hosts don't provide breakfast with Private Rooms.