Kurapia is my one of my favorite groundcovers, simply because it is a fabulous alternative to lawn. You can walk on it and so much more. It's really hardy and once established requires minimal water and maintenance. You can mow it to mimic the look of lawn or just let it be.
It typically gets no more than 1' tall and blooms most of the year. Because it blooms, it will attract pollinators. This is why some people who may be allergic to bees chose to mow it right as it is about to bloom. But you don't have to. You can just let me do it's thing.