Do you love any plants that are weeds? The definition of a weed is a plant growing out of place.
A very long time ago, I planted a wildflower mix which did well for the first two years. Then the patch gradually died away to dogs, grass, and sumac that took over. I still notice some yarrow growing through the grass (green ferny foliage with white flowers) which I mow around.
In the annual flowerbed, there is a loosestrife plant which you can not buy in most states because they overgrow in wetlands. I leave it because it is very attractive and has never set any seed and you can not call this area a wetland. Loosestrife could never compete with the cattails anyways.
There is a boxelder tree growing in a spreading juniper that I left. We do not have any boxelder trees around for miles. This one is a male, so no bugs. Also, the yellow-leaf elderberry plant sprang up the pathway to the house. I will leave that one also. Plus, the honeysuckle that is growing on one end of the lilacs.
Under the tamarisk tree is a gooseberry plant that planted itself a couple of years ago producing loads of gooseberries. When I was in high school, we had a gooseberry patch that gave out 40-plus years ago.
These volunteer plants started with no help from me. No extra watering, fertilizing, or maintenance. They go stronger and more vigorous than the plants and shrubs I spend years caring for. So, why not give them a chance?