Besides the 2 tvtropes links I gave: Link 1, Link 2...
I can't speak for partial covers for Romm from Mieruko-chan, but as for full covers like Yuusuke's dad from Koi to Uso:
Eyes are said to be windows to the soul, and the way we recognise others is through their eyes, so the lack of eyes suggests
I think the bangs are to cover up the eyes to
Case 1: de-emphasise the character's/characters' importance either to the reader/viewer or to another character/s or
Case 2: to show how such characters are viewed by other characters.
Obviously for Yuusuke and Yuusuke's dad, it's case 1.
Here are 2 examples from Kaguya-sama s2 but instead of bangs, they just don't have eyes:
S02E06 re Miko Iino and the elections
Initially, Miko doesn't see the others' eyes. I view it as that Miko sees them as arbitrary haters but then later comes to realise their were Miko's (political) fans.
In this case, I guess it's just Case 2.
S02E11 re Yuu Ishigami and the cheerleading team
Initially Yuu Ishigami doesn't see the members of the cheerleading team with eyes. I view it as that Yuu doesn't really see them yet as colleagues/friends but then later does when they see how supportive they are.
In this case, I believe it's both cases given how some of the characters play bigger roles in s3.