The FZ6R is an inline 4 600cc motorcycle but it is not a supersport. It falls into the same category as the Ninja 650r and SV650. Good sporty motorcycles that fall into the upper end of recommended motorcycles for beginners.
However I think every other 600cc motorcycle available and the ones getting the most attention are supersports so it is easier just to steer most noobies away from 600cc I-4s unless they particularly mention an exception.
And I totally agree with your assessment. I love riding my Ninja 250r. I don’t think I will ever get bored with it because it is too small. I would consider other motorcycles just for the change.