I can respect your fears, but what would you have happen if the Bard character didn't have this feat, had a 20 charisma, and let's say level 9 so proficiency is +4, and intimdation expertise.
Bard rolls intimidation at +13 and rolls a 28 total against the Balor who can't roll higher than that. You aren't required to give it the Frightened condition because they did not take this menacing feat, but what would you do?
If you say it is scared of the Bard, how is that different from Frightened? Would you ignore their roll and just have the Balor act normally?
If what is at issue here is that this ability specifies that they suffer from the Frightened Condition, then what is your solution when the Bard achieves the same numerical result on the same roll that is better.
Do you just never allow them to intimidate something bigger than themselves. I'll admit, I've broken with PC abilities like that before. Jumping out and yelling "boo" isn't going to scare something forged from the darkest depths of the Abyss that has caused the end of nations, but mechanically what can you do other than make them immune to fear (which frankly they should be, they are the biggest demons in the book)