I'd just be cooking typical BBQ food. Burgers, Sausages, chicken thighs, drumsticks, jacket potatoes etc. Nothing fancy.
The reason for not just wanting to stick the grill on top of the 'pit bowl' is to make it easier to adjust the temperature, but more importantly, I've noticed that fire pits go through wood a lot quicker than charcoal. So the tripod setup also makes it really easy to add new wood.
TBH I think you'll get a bit frustrated trying to cook that type of food on that set up.
I'd want something more stable for flipping burgers and less chance of sausages and drumsticks rolling into the fire.
As others have mentioned you need to cook over embers not a flaming fire. You can control the temperature by shifting the embers around to get different heat zones. You'll also need space to burn more wood down.
A 57cm charcoal Kettle BBQ can do pretty much everything from the usual burgers and sausages, to rack of ribs, to 10hr cooked pork shoulder and even longer for brisket. Add a rotisserie, a plancha, a Vortex fuel dome, a slow n sear and the possibilities are endless.
It's all about using direct and indirect zones and usually keeping the lid on. Cook to internal temperature not time.
That said, meat cooked over a wood fire is probably the pinnacle of live fire cooking.
I'm off to Austin, Texas to try some in May.