This is not a platform issue, it is done on purpose to deceive the customer, especially the less tech- or financially savvy customers. People have been complaining about the cleaning fee ridiculousness forever. Airbnb could and should limit the total allowable cleaning expenses (for type of house, room, location etc., in one word: localization), but they don't do it because it would decrease revenue, not because of technical difficulties, please.

The base price could be cached and then multiplied by the number of nights plus the cleaning fee before the map is rendered. I can't imagine that would be too expensive to calculate on the front end.

The price is included in Europe because EU asked them to.

When I search the map shows me a price per night for the amount of nights I picked including the corresponding part of the cleaning and service fees.

So it is not an "engineering problem" but a 100% deliberate "dark pattern" choice on AirBNB's part.