Why doesn't pandas reindex() operate in-place?

reindex is a structural change, not a cosmetic or transformative one. As such, a copy is always returned because the operation cannot be done in-place (it would require allocating new memory for underlying arrays, etc). This means you have to assign the result back, there's no other choice.

df = df.reindex(['e', 'd', 'c', 'b', 'a'], axis=1)  

Also see the discussion on GH21598.

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The one corner case where copy=False is actually of any use is when the indices used to reindex df are identical to the ones it already has. You can check by comparing the ids:

id(df)
# 4839372504

id(df.reindex(df.index, copy=False)) # same object returned 
# 4839372504

id(df.reindex(df.index, copy=True))  # new object created - ids are different
# 4839371608