That warrants a plain old "why". What would be the advantage you see in that plot twist?

And why do I think that would be pointless? I only know the Brotherhood incarnation but it is made very clear that Father tried to make itself perfect by expunging from his soul the Seven Deadly Sins, which are traits or tendencies only humans can develop. Sins are by default moral options underlined by a notion of good/bad, something other animal do not have. Animals understand something as good or bad from the consequences and outcomes a given action returns.

By contrast, humans have the notion of good/bad as our much more complex brain can project and predict consequences from a given option. This makes the humans eligible as Philosopher's Stone ingredients because of thar extra sophistication.

And while writing this I remember that ar some points Roy Mustang talks with the souls trapped in the Philosopher's Stone inside him to know if the souls are willing to allow him to use their power. The human conscience is apparently still there, which might also be a clue for why humans are material for stones and animals are not.