Quite the romantic notion of wildflowers spontaneously blooming in your unkempt yard when the best you're likely to get is crabgrass.
Past July though it looks pretty shitty.
If I let my yard grow wild then I quickly have a large variety of wildflowers, interesting plants, and mixed wildlife in my yard.
Once an environment has been altered or landscaped in anyway, it requires what is considered neglect (and/or a lot of work) to get it back to a natural state. For most people with any sort of ever manicured yard, it's simpler to mow. Otherwise by modern standards it can be unsightly, is mostly socially unacceptable, considered bad for property values, etc, and it can also minimize the human use of a field.