It's critical for many scientific simulations: fluid dynamics, finite-element analysis, that sort of thing. A few years back I was helping try to track down and buy "outdated" K80s (or were they K40s?) to run a big FEA project because they still had the best FP64 performance reasonably available despite being otherwise outclassed.

It is much easier to list the very few (but very important) applications for which FP64 is not necessary: machine learning/AI, graphics and video and audio processing, other digital signal processing.

The list of applications for which FP64 is required is huge, but they are less known because they belong to scientific/technical computing. Any design engineer would use such applications, but most programmers and non-professionals would not be familiar with them.

And the military:

https://www-users.cse.umn.edu/~arnold/disasters/patriot.html