Thank you for replying, Baja_Costero.
Although the species are different, you may have answered some of my questions. More experimentation will be needed to see. The patches of Delosperma cooperi around our place are well-established and receive full sun most of the day, as well as very little water to no water. The direct sunlight might explain their shorter stems. Also, with more leaves packed together that might add resilience to foot traffic, especially given that those patches aren't watered regularly. Unlike our young plants, which aren't used to the heat and lack of water, maybe their leaves have grown tougher.
Anyway, I'm hoping to see more feedback. Maybe someone has experience with this particular species and is willing to share.