If the story a game is based on is compelling, players may be more willing to overlook the use of common (and possibly uninspired) mechanics. The trouble with this is that there is no one story that will appeal to everyone. Thankfully there exists many tales in literature that have withstood the test of time. While they still might not appeal to the everyone, fairy and folk tales are popular enough that they are a go to when brainstorming ideas for new projects. Along with their enduring popularity, the lore and plot of most fairytales are well understood by their respective cultures (e.g. Grimm’s Fairy Tales in Western/Euro-centric cultures, or The Panchatantra in Indian/South Asian cultures).
This established understanding presents a double edged sword when using fairytales as inspiration for games. The benefit of this approach is the audience already knows the background and motive of the characters, which means less time needs to be allocated for exposition. This is good news for gameplay, since designers get more time to focus on it and players spend more time engaging with it. The downside to this is that outcome of the conflict is predictable. Audiences know how the story ends, so they will likely not be as invested as they would with an original story. Thankfully, there are multiple ways to minimize this drawback.
One of the great things about games is their mechanics allow us to explore and interact with scenarios in a way that is not possible with other mediums, such as art or writing. This means that the possibilities for telling an established fairy tale a different way are greatly expanded. The player can take the role of someone other than the established protagonist, or play as a totally new character who changes the outcome of the original story. They may even step in the shoes of the villain, which can lead to the player having to commit atrocious acts or getting to see the villain in a more positive light. Games can also expand the upon the setting where the story is set, taking the characters to places they otherwise would or could not go and dealing with the wider impacts of their actions. With how much potential games have for breathing new life into well-established stories, I think game designers should not shy away from looking to folk and fairy tales for inspiration.