One of the things I found from running DH is that you make fewer rolls in it than in other games (like 5E). This means any individual check means more. If you only make three checks all game outside of combat, three fails with fear can have more of an impact. In a typical 5E session (and I just played in one, so it's fresh in my mind), you roll the dice a lot, assuming your DM isn't coming over from a PbtA game (or DH!) I think that's the cause for a lot of the comments on how bad the dice system can feel.
The thing is, it's usually just one session, and over a campaign, you'll see how you succeed more often than you fail, but if all you're playing is the quickstart, the GM should think about it.
What I did, behind the scenes, is tally failures for each player. If they happened to fail three times in a row, I was prepared to narrate something happening and give them a Hope. In the game I ran, this never occurred so my rule never came into play. And yes, I suspect you might think this is unnecessary, but I am the nice one.