We live in the country (southwestern PA) and only keep about an acre or so around our house "groomed". The rest we leave for Nature to landscape. The field in front of our house is cut for bedding hay by a neighboring farmer. He hasn't gotten to it yet and it is full of Queen Anne's Lace. I love looking at it. In some areas we have Queen Anne's Lace growing with chicory. (I called it cornflower when I was young because the flower is the color of Crayola's cornflower blue crayon.) The combination of the two plants is beautiful.
At our previous house in the suburbs I had a garden bed under an old crabapple tree. One year I didn't get to the weeds and we ended up with lots of Queen Anne's Lace. I thought they were so pretty that I left them in when I pulled the rest of the weeds. The neighbors thought I was nuts, but I didn't care; that bed was perfect.
As far as being invasive...I think Queen Anne's Lace is way more controllable than Japanese Knotweed! I HATE Japanese Knotweed. It is next to impossible ("next to" as in "sitting in the lap of impossible") to irradicate. I have been fighting this plant since we moved here. If I could replace it all with Queen Anne's Lace and chicory I would do it in a heartbeat.