Weight could be a crucial consideration in not simply sub flooring and the tiles themselves, but also in the structural elements of those struts which actually support the floor itself. It is entirely possible you have your heart set on that Brazilian slate flooring and that hot weather would mean partially rebuilding the structural underpinnings of the kitchen! It's not that bad though. Even that is definitely do-able, Stone Veneer so fear absolutely not.
The main benefit employing real rock is in which it lasts almost forever. It is 10x to the extent of asphalt shingles, but slate roofs last 10x since well. Needed much less maintenance Denver roofer over that span also. Like tile, slate particularly heavy and a sturdily built roof to hold it " up ". Not all roofers are well-versed in slate.
Slate certainly a versatile building material.