Let me get this straight – you believe that oen should daven b’yechidus WITH a hat, rather than in a minyan without one? We are always taught to daven in a minyan, because while our own zechuyos may not be sufficient for Hashem to answer our tefilos with a “yes” it may be that someone else who is davening is VERY worthy, and in his zechus Hashem will show Rachamim to the less worthy person as well.
It’s okay, Oomis, you don’t ned to wear a hat to daven. 🙂
And yes, this is a serious shaila. Although Rav Elyashiv is quoted as saying that it’s more important to daven b’tzibbur, R’ Chaim is quoted as holding the reverse, and he is not the only one who holds this way.