Lawns are for much more than just flexing. It's an outdoor part of your property which is flat and open enough to use for various activities and purposes. I don't know where people get such a cynical idea that this is THE reason anyone has lawns.
There’s definitely more to the story and there are myriad factors.
There's plenty of evidence the rear gardens were used for growing food and drying laundry back then
Children would also play there where they could be seen from the kitchen (which was always in the rear), rather than playing in the road (as much)
Rear gardens also served as a space where you would converse with your neighbour. Typically fences between neighbours were low and wire (tall 6ft wooden fences came later)
The other thing is the only toilet in a 4 bedroom property would also be out there, as an outdoor WC, accessible from outside
I doubt much read space was reserved for lawn back then
The neighbourhood of "Cabbagetown" in Toronto is so-named because yards were not used for 'ornamental' plants:
> Cabbagetown's name derives from the Irish immigrants who moved to the neighbourhood beginning in the late 1840s, said to have been so poor that they grew cabbage in their front yards.[2] Canadian writer Hugh Garner's novel, Cabbagetown, depicted life in the neighbourhood during the Great Depression.
I've lived in a few row houses with fully paved outdoor areas. I don't really see the point of that either, but at least it doesn't require regular maintenance so it only has to be occasionally useful to come out ahead.