Times when the secret hunting made the game actively worse?
And I don't necessarily mean in a mind-goblin type way, but in a mechanically frustrating way that makes the main game worse to play if you partake.
Say, for example, Mega Man Legends 2.
The game has a lot of destructible walls in it. As in, roughly half the dungeons have one. And behind those walls is guaranteed weapon parts that you need to build several different sub-weapons. And they're super obvious so you'll probably just be able to eyeball it while you play the game normally.
However, the only way to break the walls is to equip a specialized Drill Arm sub weapon, which has effectively no range and is generally pretty weak. You have to try really hard to use it effectively in combat and you can only equip one sub weapon at a time. So in order to break the walls you have to get to the wall with effectively only your main buster.
On paper, this is a fairly straightforward risk/reward setup. By turning down your potentially more powerful and more conventional sub weapon, you get access to extra weapon parts as a reward.
The problem is, every ruin could have a hidden wall, so in order to build your arsenal up and even have access to the fun weapons you need to basically turn off your sub weapons entirely since you didn't know walking into the ruin whether the Drill Arm was even needed. So you ended up NEVER wanting to use any sub weapons even as you built them even if the ruin you were exploring didn't have any secrets. And it's not like sub weapons were critically important. Your buster does the job very admirably even if it takes a little longer. So the games secret system had the same effect as items in Devil May Cry, as in, you built an entire system that you get pushed not to use.