If I own a house (outright) and live in it, I pay nothing, and no impact on GDP
If my neighbour owns a house (outright) and lives in it, I pay nothing, and no impact on GDP
If I rent from my neighbour for $10k a year, and he rents from me for $10k a year, GDP increases by $20k a year, but nothing has really changed, expect the amount of money paid in taxes.
So that's why you have imputed rent as part of GDP. Fine, I get that.
How about this scenario
I have a kid and look after it, I pay nothing, and no impact on GDP
My neighbour has a kid and looks after it, he pays nothing, and no impact on GDP
I look after my neighbours kid 3 days a week and he looks after mine, in an exchange, no impact on GDP
I look after my neighbours kid 3 days a week and he pays me $300, and he looks after mine 3 days a week and I pay him $300. GDP increases $600 a week, and more money is taken in taxes.
Do we include all unpaid work?
If I (a painter) pay my neighbor (a gardener) to garden my front yard and he pays me to paint his garage, then GDP increases.
If I do the gardening myself, and he does the painting himself, GDP doesn't increase.
How about me looking after my old parent vs me working overtime and paying a care home to do it?