Mine is slightly different from the other responder. I do mow my front yard (HOA requires it), but in the back I only weedwhack the areas that we actively use and a path to them. The gondola does have a square of cheap Home Depot astroturf under it, mostly so I don't have to weedwhack it every time we want to use it.
My back yard is primarily ~knee high hedge parsley at the moment; the flowers are beautiful! I will have to weedwhack most of it here shortly though. Hedge parsley grows burrs after blooming, and it's a huge pain to pick them off all my clothing and furniture after my dogs roll in them and then come inside.
My dogs love to run in it, and it brings in ton of wildlife. I'm on the edge of urban and suburban and get deer, rabbits, tons of birds, squirrels, raccoons, field mice, and more insects than you can shake a stick at. The mosquito population is surprisingly moderate as well; my suspicion is that the natural plants provide enough food for herbivorous insects that my house has a standing population of carnivorous insects flying around.
I vastly prefer it from an aesthetic standpoint, though I grew up rural and prefer the organized chaos of nature over the unsettling uniformity of manicured outdoor spaces generally. It's also much less work than routine weed-eating and what not. Some people may have allergies and hate it.
My only major concern is with attracting dangerous wildlife, primarily snakes given my geography. There's nowhere particularly warm for them to bask, but hiding spots are innumerable. Humans would likely be okay (the hiding spots are not close to where we hang out), but I do worry for my dogs. They really like sticking their snouts places where snakes would like to hang out.