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Due to the nature of your game, I'd say it is a good idea, and many games already do do this. The first one that comes to mind is 999 (9 Persons, 9 Hours, 9 Doors) in which you have to do exactly a...
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Source: https://writers.stackexchange.com/a/33148 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
Due to the nature of your game, I'd say it is a good idea, and many games already do do this. The first one that comes to mind is 999 (9 Persons, 9 Hours, 9 Doors) in which you have to do exactly as you are stating- gain knowledge from past play throughs to get the "true" ending. Giving one true ending is also especially common in visual novel sort of games. Usually with these sorts of games, especially considering that you're encouraging players to get all the endings, the game is only really completed once completing all the "bad" endings to successfully run the "true" ending. The only catch really is to not make the bad ending too unrewarding, but it sounds as though you are aware of that. Overall I don't think it's bad game design. A player who is really experienced in these sorts of games could always look up the decision tree and just jump to the true ending. I'd suggest maybe a warning at the beginning of the game that your actions will affect the game outcome, as well as a "skip" feature for text/content the player has already seen. Best of luck!