You hit on a really important point here, which is contextualization of hints and when it is important to do so. It definitely requires thought in the design process in how to incorporate the hint system and to do so in tandem with the development process instead of after the fact.
What I love is when a game’s setting and design allows for the hint system to be incorporated in a way that makes sense within the world itself. A fixer in your earpiece on a spy mission that can offer clues and outright solve the puzzle for you if you just can’t get it or a magic spell that provides insight into the task at hand. We can make hints be more enjoyable and actually fun to utilize in a way that makes the player feel smart without shaming them.
On the reverse side, some games don’t have the opportunity to contextualize hints within the world, but a lot of times, the style of the game isn’t really trying for immersion.
In the end, making games is hard. Making games that help players without it being at the expense of pace is even harder. This is why communities like Intfiction here are so valuable because it is a pooling of knowledge that can help developers design better. So I guess the most important step to figuring out these problems is asking the questions and I am glad folks are!