"Recreational"
lol no that's not how this works
Terpenes are in basically everything that grows from earth. They can have their own non-psychoactive health effects, or in the case of marijuana they can modulate the effects of the cannabinoids. [that at least seems to be the suggested method of action at this point]
As for coffee: what you are describing is called "Turkish coffee." Prepared like most variants of something like a french press (grounds fully immersed for steeping during the brew, unlike a drip-type maker) but it doesn't have the filter step at the end.
Yes you could say it's a touch more natural, but filtering for teas and other brews has been part of the otherwise common steeped extraction process, and has been for ages. More rudimentary as you go back in time, but of course it was patchy in reality, as some areas would do it whereas others either never thought of it or never cared or found themselves bothered enough.
You generally weren't going to drink/consume the grounds in the end, not in large quantities mind you. Typically brews were of larger quantities in ancient times, as you poured you generally decanted and naturally kept much of the grounds at the bottom of the cooking and/or serving vessel as the liquid was portioned out.
As for the natural properties, you don't need to keep the grounds, you just need to mind the filter. I *think* different paper filters tend to invariably block extraction of some of the terpenes and flavonoids. But a mesh screen won't block the chemical molecules, just the majority of the particulate matter (i.e. the grounds).
[and back to marijuana, some flavonoids and especially cannaflavins (those flavonoids unique to cannabis) may even be key to some parts of the entourage effect as well as pharmacologically active in their own right.]
In other words, you don't gain anything natural by keeping the grounds when compared to the more rudimentary filtering methods. I mean you can gain some more potent flavor, sure, because the steeping is constant even in the cup -- but more often than not, you don't tend to want the more bitter extractives that generally don't leech out during less prolonged exposure to water. I highly doubt too many of these are beneficial terpenes or flavonoids though I haven't dug too deep into that research topic (if that's even been explored before...).