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From the perspective of game logic, removing the morale of neutral creatures is nonsensical. Either morale should work for everyone according to the general rules, or it should be removed altogether (which, of course, won't happen).
It is clear that the morale of neutral creatures has a negative impact on balance. But this is not enough to drastically violate the game logic. Moreover, the idea of removing the morale of neutral creatures is not that popular even among multiplayer players, let alone single-player players.
Theoretically, I can imagine a scenario where the template settings could be used to specify the presence of the "spirit of despair" for all players from the start. Then, accordingly, it would be possible to create "immoral" templates.