I get it. There are some players that absolutely won't meta game but I feel like secret rolls aren't for those players. It's for those that can't help but metagame. I have a player that is literally incapable of not metagaming. In a 5e game I was running I had a player get charmed by some kind of monster effect. This caused his character to swim out towards the monster. I informed him that he could reroll the save after he takes damage. Just so he could know when to reroll. The problem player stated that she was going to keep shooting her teammate until he broke the charm despite her having no information on the charm or even the existence of what caused it. All because I told the other player about when he could reroll. Don't get me wrong, if a character suspects a charm in 5e then hitting the teammate out of it isn't a terrible idea but her characters only information was that her teammate was in the water despite other teammates also being in the water at the time. In the 5e campaign she would consistently metagame in other scenarios as well.

She has been having a much easier time in pf2e because she doesn't have the information to metagame with. Her ability to role play has improved phenomenally because she just resorts to what her character knows because that's all she knows too.