Ground cover for hard dirt?

Every cover I can think of probably will choke out other plants. Usually it's vines of some sort that can find enough dirt among the rocks to root in and cling to the rocks with tiny tentacles. Creeping Charlie, any ivy, kudzu, blackberry bushes, will all be groundcovers, but they claim the ground they cover. Best wishes 😇

Monkey grass, purslane, and sedum. They don't need much root depth and they spread fast. The purslane has beautiful flowers and it's edible.

Before one can answer what is your exact location?

Sun/shade? Soil? pH? At elevation in arid New Mexico in dry shade I like native geraniums, vinca, leadwort, the non-invasive tansy. In sun, sedums, ice plant, catmint,alkanet, creeping germander--and some of these are super, super hardy. If you're in Utah these would probably work for your soil too, but the southwest has lots of issues so location, zone, micro climate, elevation, wind, pH--these play a bigger role here than back east. Check with your local Extension and Native Plant Society for recommendations that woul nail it for your conditions.

moss rose, (has flowers) portulaca is the real name