You are correct that this is technically in code and would protect against shock hazards in a neutral error situation but you also get the opportunity for the outlet to pop during the day when nobody is home and the battery to die.

We had a situation in our old house where someone who was technically correct but didn’t think it through had a gfci outlet upstream of the refrigerator outlet. Thankfully it popped while someone was home and we got everything corrected before we lost everything in the fridge.