Carbon stem seems to be way into weight weenie/carbon bling territory. Other than shaving a few grams off your bike and wallet, I can't imagine there's any real benefit. If a stem is flexy enough to provide any actual "compliance" benefit, then it seems like it would make for some super weird handling.

I do like carbon handlebars and have a very fancy carbon bar on my CX/Gravel bike. I run it with an alloy stem.