Premature Ends are Necessary
Let’s say, conservatively, all your choices have only two options and no more. Suppose every path through the game lets you make ten choices, and every possible branch you can take is unique.
You would need to write 2,047 unique branches and 1,024 unique endings. If each screen has about as many words on it as the pages in Wikipedia’s list of longest novels, that would put the number of words you’d need to write in between War and Peace and Romance of the Three Kindgoms.
So, out of necessity, you’ve got to limit the exponential growth of your story branches. Either multiple paths all lead you to the same branch, or most of the choices you could make end the story prematurely. Typically, if you’re ending the story early in order to reduce the number of endings, you’re not going to write four or ten or twenty premature endings off that branch and have the player explore them all to discover they’ve put the game in an unwinnable state; you’re going to say Game Over quickly. And typically, a premature end is a bad end.
Thus, the structure of those old Choose Your Own Adventure books, where pages cost real money, so most of the choices you made led to instant gruesome death.
Early Ends Don’t Have to be Bad Ends
This is really up to your creativity as a writer, but an ending just means you don’t have any more choices to make in the game. Realistically, the protagonist’s goal could be to get out of this mess as quickly and easily as possible, or at least be tempted to take the easy way out. This could be at cross purposes to the player’s curiosity about what will happen if things don’t get better—the route that keeps her in a situation she doesn’t want to be in (and you playing the game) could be the bad end! A clever videogame variant I heard about but didn’t play: you start out infiltrating a terror group, they ask you to do various things to prove your loyalty, and the way you keep playing the missions to the end of the (linear) story is to keep playing along with them long past the point where it’s an act, becoming the Big Bad of the game. Actually stopping them before they kill any more people completes your mission, so it’s a Game Over. Inverting the moral valence of that: her story arc might be that she starts out just wishing for an easy way out, and you have choices that will let her do that and be content and happy, but if you keep playing long enough for her to see what’s going on, she’ll start getting more and more uncomfortable and want to change it.
You Can Merge Branches, Not Just Prune Them
Another way to reduce the branching is that a game can have state. Several different choices about what you do over the weekend can all lead you to go back to your normal routine on Monday, but the game can remember that you’ve had different experiences, and that can lead to different outcomes later.
This is the structure of a lot of life-sim games, where most paths through the game take you to the same place at the same time, and then it determines which ending you got based on all the things you did.
Do too much of this, though, and the player might feel you’ve given them false choices that don’t really matter.
A Bad End is in the Eye of the Beholder
Pretty self-explanatory, What’s good for the protagonist might not be a good outcome for the world, and vice versa. She might change her mind about what she wants. We might think the “best” ending is one that gives her the most compelling moral arc, or where she finds out the unpleasant truth, or where she meets her true love, or where she achieves the most glory, but those might not be the only endings that make her happy. And several different happy endings could be long and developed branches that could go wrong in multiple ways. That gives your game replayability even after the player has “won,” beyond seeing all the deaths.
Yes, I would suggest that you find a different story structure. That one is overused.