- It's going to look weedy fast. Without design intention your neighbors will be less apt to get on board.
- Invasive species may establish. What's in the weed seed bank? You don't know. Could be some native plants -- likely aggressive seeders -- definitely going to be aggressive exotics.
- Woody plants will move in. Without constant management tree seedlings will start to grow. This could be an issue if you live on a small lot or in an area where forests aren't a habitat type.
The point of this post is not to push you to some hyperbole, like "well then what should we do, slather the lawn in chemicals?" It's to get you to think intentionally about your space -- from design to succession, to what you ideally want to happen and to the big leaps your neighbors will have to make when you break from the status quo.
Over the years much has been shared on this website about designing a landscape -- from plant selection (sociability and size) to plant succession over time. When you let your lawn go or stop mowing, there's seldom a plan that takes into consideration management or neighbors. So if you let your lawn go, think hard about a management plan that takes into consideration your ecoregion and lot size, as well as your environmental and community goals. And know your plants.
If we're not working smartly with a plan and a goal, then we're just being lazy and ideologically polarizing for no reason. That's not helpful or neighborly.