The inconsistency with GNU date is more visible from Feb:

  $ date -d "jan 31 next month"
  Wed Mar  3 00:00:00 PST 2021
  $ date -d "jan 30 next month"
  Tue Mar  2 00:00:00 PST 2021
  $ date -d "jan 1 next month"
  Mon Feb  1 00:00:00 PST 2021
  $ date -d "feb 28 next month"
  Sun Mar 28 00:00:00 PDT 2021

Edit: This was on my unconscious mind for a bit and I came up with an additional test case to confirm a suspicion I realized.

  $ date -d "2016-1-31 next month"
  Wed Mar  2 00:00:00 PST 2016
  date -d "2016-2-1 next month"
  Tue Mar  1 00:00:00 PST 2016
  date -d "2016-2-1 next year"
  Wed Feb  1 00:00:00 PST 2017
  $ date -d "2016-3-1 next year"
  Wed Mar  1 00:00:00 PST 2017

GNU date will add the duration of the CURRENT interval (ignoring already occurred deviations, like leap years) relative to the specified base date.

The oddity in behavior I observed above is adding the length of the month of Jan to dates in Jan. I suspect only a programmer would find that inference remotely correct.