Of course it will if you cut and cart the future nutrients away each week while creating 'greenery' that is a monoculture entirely unattractive to animal life.

As long as you've got a water source, you can easily create a tiny patch of green that can survive for decades unattended - even in the midst of a desert.

Agreed, it's a struggle. We apply milorganite or similar biosolid product every third month to ensure the grass gets the nutrients it needs. Otherwise we get a spotty lawn, which in turn results in poor water retention and pooling.