I think you’ve shown equivalence? 100 shareholders own ($1 cash + $99 in stock) or 99 shareholders ($100 in stock) and one former shareholder ($100 in cash). (Not trying to be snarky here. Appreciate the answer.)

Gone out for a reputable source:

CFA [1]

John Cochrane: “That was the big point. Share buybacks are a good way to get money out of firms with no ideas, into firms with good ideas.” [2]

[1] https://www.cfainstitute.org/en/membership/professional-deve...

[2] https://johnhcochrane.blogspot.com/2018/04/buybacks-redux.ht...