The reason households do not have an inventory is not that recording things is hard. It is that handling every object in the house is hard, and nobody is going to do it as a standalone project.
Except once a year, when they do
A deep clean already involves moving everything. The marginal cost of photographing the serial plate on the machine you have just pulled out, or noting the model of the thing you are dusting behind, is close to zero. The expensive part is already being paid.
What to capture while you are there
Model and serial numbers on anything with a motor or a heating element. A photo of each room, wide, which is worth more to an insurance claim than any list. Anything under warranty. And, honestly, anything expensive enough that you would have to describe it to a stranger to replace it.
An inventory taken on a normal day is a chore. Taken during a clean, it is a byproduct.