It's not surprising that LSAT scores are higher due to the additional time to prep and the ability to control the testing environment. And in reality, it doesn't matter that much. Schools will sort students just like they always have, and students will end up roughly where they otherwise would have. The whole application process is on a curve.
It's also worth noting that over the last decade, it's been increasingly easy to get into prestigious law schools. Students got wise to the fact that law school costs a ton and many students don't get high-paying jobs. As a result, applications went down and lower-scoring students got into better schools. In some ways, this most recent stat may be mostly a reversion to the prior mean.
How much does the LSAT saturate though? The SAT, particularly the math section, is already very saturated at the top percentiles, which make up almost the entire application pool to the elite schools. That's why those schools basically just use the SAT as a quick screener now, if they use it at all. Raising scores even more would further diminish its utility and could increase the impact of a silly mistake.
The LSAT isn't nearly as saturated at the top. As the article mentions, in normal years there are only about 700 applicants in the 175-180 range (roughly the top .5%). Compare this with the SAT, where there are over 50,000 students annually in the 1500+ range.
Even at Harvard and Yale Law, the median score is outside this range (173), and all other schools have a lower median.
It's also worth noting that over the last decade, it's been increasingly easy to get into prestigious law schools. Students got wise to the fact that law school costs a ton and many students don't get high-paying jobs. As a result, applications went down and lower-scoring students got into better schools. In some ways, this most recent stat may be mostly a reversion to the prior mean.