These days it's rare unless an existing highway (like I-85 or I-95) is being widened. The Northern beltway in Winston-Salem has a grass median. Pretty much all new freeway segments have a grass median when built. Although I-85 in Salisbury was widened and they used a grass median and not a concrete barrier.
In North Carolina, most new freeways are built with 46-foot medians, enough room to add two twelve-foot traffic lanes plus ten-foot left shoulders and a two-foot-wide concrete barrier. They've been doing that on various projects since the eighties, as I and others delved into in
this thread. I was amazed to learn that that includes virtually all of I-40 from Raleigh to Wilmington, which is highly unlikely to ever require six-laning. A case could be made, then, that virtually all new freeways in North Carolina are designed to eventually have a concrete median barrier. It's not rare at all.
One problem with that argument is that there are seemingly-similar cases, such as I-85 near Salisbury and, more recently, I-85 south of China Grove versus at Spencer, where barrier-now versus barrier-maybe-later were chosen for (to me) no obvious reason. My uneducated guess would be that, once it was decided that the once-somewhat-standard 68-foot width needed a cable rail barrier, might as well narrow the median to 46 feet and provide a slightly-more-expensive two-sided W beam guardrail instead. Or, in the China Grove vs. Spencer case, it may have had to do with construction phasing depending on the original median widths: narrow at Spencer, sixtyish south of China Grove.