Can you prove that monika's plot manipulation works via thought? In pretty much all of her 4th wall bending abilities that we see her use while onscreen (or while her presence is nearby), she types a command in a terminal.
Monika did survive being erased, but the fact that she experienced extreme pain as a reaction to nonexistence is an indicator if anything that she cannot survive it for very long. If Chara were to erase her, she could have time to try to erase Chara back, but Chara would likely just... chill out and monologue.
As you stated, Chara likes talking. This could potentially give Monika enough time to attempt Plot Control on Chara, but keep in mind... The dialogue of DDLC is canonically a script that remains set in stone unless ****** with. None of the characters in DDLC, with the exception of Monika, are "real" according to Monika herself. All she had to do was edit a few lines of code to change what they'd say or their personality traits. Chara, on the other hand, is not from the DDLC universe and is not canonically just a script, so we can assume that she *is* real, and due to the way Monika's Plot Manipulation works, she wouldn't be able to Mindhax Chara.
In the end, it does come down to them both erasing each other. Chara can survive nonexistence indefinitely, and Monika has no way to conceivably take her out. Chara, on the other hand, can erase her and the whole universe. If Monika backs up her file, Chara can just erase her again and again and again while incorporeal until Monika decides that the painful sentience she's forced to suffer through isn't worth it, accepts her fate, and doesn't back up her file.
