Where did you get the impression that a good moving TB is a leg flinger? Or did you just mean that some of these modern horses (in part due to the riding) aren’t using their back legs properly?
IMO elasticity comes from self-carriage which starts with a pushing and carrying hind leg.
A good TB may not best for sitting down and carrying at the trot (although I have seen a few – meaning I can think of 5 off the top of my head that I knew of IRL), but they always bring the push.