This makes sense because under compound symetry, every measurement within a cluster is correlated in the same way with all other measurements. Therefore, adding another observation within cluster provides less information as the number of within cluster samples approaches infinity.

However, when we have an auto regressive correlation structur, the further apart the time point, the less correlation there is between samples which means the sample tends toward zero.

The random intercept model induces a symetric correlation structure that leads to the idea that the measurements within subject are exchange able.

A random intercept model assumes that the correlation between any two measurements on the same subject is unrelated to the time gap between the two measurements.

Thurner, S., Klimek, P., & Hanel, R. (2020). A network-based explanation of why most COVID-19 infection curves are linear. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.2010398117

Mehrotra, S., Rahimian, H., Barah, M., Luo, F., & Schantz, K. (2020 May 02). A model of supply-chain decisions for resource sharing with an application to ventilator allocation to combat COVID-19. Naval Research Logistics (NRL). https://doi.org/10.1002/nav.21905