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 &amp; 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)