Looks like a bug under High Sierra.
Repro
1. Close any open Quartz graphics window
2. Running the example on the top of the cowplot page you linked.
Obtained: useMethod("depth") error when the second plot tries to render (no
need to resize the window)
Running the code a second time (i.e., when
Tim,
I've run the example code on the page below and resized the plots with no
errors.
https://cran.r-project.org/web/packages/cowplot/vignettes/plot_grid.html
It may have something to do with running High Sierra, or the specific
code/data you are using.
Could you post a reproducible example?