I don't think LACs are "dying" (which would imply a decline in performance) moreso than other universities are climbing- especially those in urban areas. Schools like UChicago, Northwestern, Rice, Vanderbilt, USC, UCLA, Johns Hopkins, Tufts, Northeastern, and such are getting more desirable.
Students want large experiences in or near urban locations. The LACs which have seen the greatest increases in yield are Barnard (Columbia University consortium, NYC), Wellesley (MIT consortium, Boston), and Pomona (Claremont Consortium, LA). Swarthmore's perceived intensity and lack of use of the consortium undermines to prospective applicants the access to UPenn or Philadelphia.
But the yields and selectivity have remained consistent at Amherst, Bowdoin, Williams, Carleton, Swarthmore, and the like. That means there are always those who will enroll at these schools.
https://www.swarthmore.edu/sites/default/files/assets/documents/institutional-research/AdmitYieldRatesChart.pdf
Swarthmore's yield has been ~40% for the past 17 years.
https://www.haverford.edu/sites/default/files/Office/President/Factbook-Admission-Stats.pdf
Haverford's yield has been ~40% as well.