Is there an optimum (or minimum!) thickness for a steak when cooking on a BBQ?

It really depends on what temperature you'll be grilling these steaks and for how long. You could do it with 2cm if the grill is hot enough. Honestly, the thicker the steak the better control you have over temperature changes (it takes longer to overcook a thick steak than a thin one, since more meat means more heat insulation).

Back when I followed the excellent Science & Cooking Harvard course they provided us with a tool created by MIT students for demonstrating heat diffusion through meat over time. You can use that tool to figure out steak thickness based on grill temperature, meat starting time, total time, desired doneness, flipping technique...

http://up.csail.mit.edu/science-of-cooking/home-screen.html

(According to the tool, for a 2cm steak starting at 23°C, grilling at 150°C, flipping every 30s for a total time of 3:30 you should get your steak brown on the outside and medium rare on the inside after you take it out of the grill and let it rest for a few minutes)

Having grilled steaks hundreds of times, and keeping your goals in mind, this is what I would do:

1. Slice into 4cm thick steaks, or about 1.5-2 inches
2. Season as desired, but adding more salt than you would a thin steak
3. Place steaks on a metal pan at least 1 hour before cooking
4. Leave the pan out or in a cold oven to come to room temp throughout (!)
5. Turn steaks in pan every half-hour to ensure even warming
6. Grill steaks hot for 10 mins: 5 mins per side
7. Move steaks away from flames, "baking" for 10 more mins (5/side)
8. Pull onto tray or transfer pan, rest 5 mins
9. Enjoy, maybe with a salt patch to dip rare (aka salt-less) pieces

getting them to room or even body temp before grilling is the biggest key to having safe and delicious steaks in the manner you describe.

This is a long comment answer, but the cooking conditions and thickness combined with the outcome the user wants go hand in hand and make this unanswerable. A standing rib roast is the same cut as a rib steak, normally just cooked differently. But near me, it is not even uncommon for them to be cooked the same. I know of restaurants that pride themselves in serving grass fed Montana beef for premium prices that will put "prime rib" and "ribeye steaks" on special. If you order either, you get exactly the same piece of meat. The roast to a very rare in a slow oven, then when you order the slice a piece off, finish it on the grill to order and serve it. If you ordered prime rib, they include a side of dipping au jus, if as a ribeye, they pour it over the top slightly thickened as a sauce. To them, what thickness to cut would be answered as why are you cutting it to begin with?

In my experience, the thicker the cut, the slower you want to cook it which makes sense unless maybe you like your steak black and blue (or as it seems to me, burned on the outside, icy on the inside). But thickness, temperature, cut of meat, and what technique is being used all combine with personal taste and result is no real answer. 1 and 1/4 inch was often a standard for good NY cuts for instance where I grew up, but unless they were roasting them, no one there would cut a sirloin that thick as it would come out like leather. Where I live now, 1 inch seems standard for a NY, while I often see sirloins cut much thicker that still turn out juicy and tender. This tells me that the way the animal is raised also factors in and changes how the meat should be treated.