Yes, but that doesn't mean you have no discretion or control over what is growing and how. The key is that you want to choose things that require no supplemental watering or nutrients like most non-native lawn grasses do.
Choose native grasses that are well-adapted to your climate. This may mean dormant / brown periods of the year, but this is perfectly natural. There is a mental hurdle to clear about an aesthetic that isn't going to be achieved.
There are many native ground covers that are also available, and many that flower to provide habitat and support for animals. Both these and grasses can be mowed to an acceptable height.
Wherever possible, put in native wildflowers or shrubs/trees. These sustain other life and they look amazing.
You'll have a nice little garden in a few seasons.
We're currently planting berry bushes, nuts and clover in large parts of our yard. It's fairly low-maintenance and as a bonus the clover is and excellent food source for our rabbits and chickens.
I had no issues with erosion. The plants lived for years and established rhizomes and extensive root systesms.
I made a serious attempt to do ANYTHING but a lawn. Here are the issues-
No grass= erosion. This + weeds makes a dirt yard impossible.
If you want to 'farm' there is tremendous maintenance involved
Turf is expensive, but might have been a solution.
More concrete= hotter. This is bad for the environment.
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So is the solution to let native plants grow all over your yard? We did this for 1 year, but my wife ended this.