What has happened to make my library() just never work?

From you original post, it looks like RStudio tries to load from its own mirror version of CRAN:

Warning in install.packages :
  unable to access index for repository https://cran.rstudio.com/bin/macosx/el-capitan/contrib/3.6:
  cannot open URL 'https://cran.rstudio.com/bin/macosx/el-capitan/contrib/3.6/PACKAGES'

so maybe there an issue there? I'm not sure, but am glad you discovered a workaround!