I'm not sure I really follow how this actually will result in better lenses. Is the precision of the numerical solution really the problem, or is the problem the actual precise manufacturing of the lens elements?
I have a strong suspicion that the numerical solution is as precise as needed and the limiting factor is the manufacturing, but I would be interested to hear how this results in something new.
Your suspicion is justified. The news here is the discovery of an analytical formula - which is "precise," sure, but whether using it directly in an actual computation could yield a more accurate and practically useful result is a good question, due to the complexity of the formula.
Your suspicion is right, as far as manufacturing goes.
The real boon of this discovery is in designing lenses. For example, the authors have already used it to design a single-lens telescope for the first time [1]. I don't know much about the forefront of optics, but at least in my field having analytical models that you quickly iterate on and use to prime intuition are extremely useful.
I think the problem was being unable to solve a generalized version of the equation. Our old methods only made it economically viable to make "good enough" lenses and now this method makes it economically viable to make "perfect" lenses.
I have a strong suspicion that the numerical solution is as precise as needed and the limiting factor is the manufacturing, but I would be interested to hear how this results in something new.