To my thinking (and I unfortunately did not know Bill Grover so this is purely my thinking), Grover's "right-handed" design was probably to some extent a marketing gimmick, and a very successful one at that, given that so many other sixguns have faded into obscurity while we still talk about the Grovers. Gimmick or not, the quality and beauty of Grover's sixguns are beyond argument, and that's where my REAL passion for the TLAs resides.
Still, the "right-handed" design is neat in and of itself, and handling one becomes second nature very quickly. But switching from Colt-style to TLAs can be awkward, as I was reminded of during last week's Shootist Holiday. I shot my USFAs and Rugers all one morning, then switched to my TLA South Texas Army, and it took a little bit to come up to speed.