I get both, for what it's worth. Plenty of crabgrass later in the season, but abundant clover, wild strawberries, wild violets, and little tiny blue pansy things that I don't know the name of earlier. Bees everywhere!
I don't consider maintaining or not maintaining a yard to be romantic, it's more of a chore. Gardening is a rewarding activity, but it's also not particularly romantic, it's what humans did for thousands of years to get food.
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.
This year I overseeded with a mix of ryegrass and clover, will keep my lawn mowed at 2 inches and watered. I hope the clover can bloom at that height and make the bees happy. It should look fine if I keep it at 2 inches every couple of weeks.
It may start off that way, but after a few years, that crabgrass may decline or die off entirely due to competition from native species. Around these parts, if you let the local squirrels have at it, you may wind up with a forest instead!
Past July though it looks pretty shitty.