Well, engineers building physical systems like airplanes and rockets use Lyapunov exponents to avoid chaotic behavior. No one sane wants airplanes or rockets that exhibit chaotic aerodynamics!
Has progress stalled in this area? I don't know, but surely there are people working on it. In fact I recently saw an interesting post on HN about a new technique that among other things enables faster estimation of Lyapunov exponents: https://news.ycombinator.com/item?id=45374706 (search for "Lyapunov" on the github page).
Just because we haven't seen much progress, doesn't mean we won't see more. Progress never happens on a predictable schedule.
To add to this, a moderate amount of turbulence (a type of chaotic fluid flow) in engines and wing surfaces is sometimes deliberately engineered to improve combustion efficiency and lift, and also chaotic flow can induce better mixing in heat exchangers and microfluidics systems.
Has progress stalled in this area? I don't know, but surely there are people working on it. In fact I recently saw an interesting post on HN about a new technique that among other things enables faster estimation of Lyapunov exponents: https://news.ycombinator.com/item?id=45374706 (search for "Lyapunov" on the github page).
Just because we haven't seen much progress, doesn't mean we won't see more. Progress never happens on a predictable schedule.