This is a very good question. There are several answers, since you have asked about New Mexico in the past I will limit it to the semi-arid steppe ecosystem.
Bunch grass is a good term for clumping grasses google searches.
Allelopathy - plants in arid regions suppress competition by inhibiting germination and growth of seeds/plants near an existing plant. Rain water washes compounds off the established plant. The concentration of the inhibiting molecules is highest close to the established plant.
Some known allelopathic compounds:
https://www.cambridge.org/core/jour...ic-chemicals/80506ABB13DC975F63797B89F854DEA9
If you walk anywhere out in the scrub you will note that almost every plant species seems to keep its distance from neighbors.
(this is probably the best fit for your question)
Microclimate and plant succession - allelopathy has limits. Switchgrass (Panicum virgatum) is an extreme example. What appears to be single individual in a clump usually is not. It is often a group of genetically very diverse individuals. Stipa and switchgrass are part of later succession. They germinate best in the presence of their own species. The clump changes very local conditions enough to favor growth of its close "cousins". These species do not self-pollinate and very local individuals for pollination are a big plus for reproduction.
Plant succession -
https://en.wikipedia.org/wiki/Ecological_succession
Microclimate and germination - A local example is probably best: Go up in elevation (like 6500 feet), in order to get into the PJ's (Pinon-Junipers forest). You will find young pinon pines growing in the middle of junipers. The pines as "juveniles" do best in the conditions found under Junipers. Bear in mind that most of the trees you see are hundreds of years old, and the junipers that got them started are long gone.
Google for "fairy circles" to get some other points of view on spatial relationships of plants