Is there something inherently bad about AT328 EEPROM

I honestly did not know what a AT328 was. Since you write about Pro Mini's, it must be a ATmega328P.

There is absolutely nothing wrong with the internal EEPROM.
The bootloader can not turn it on or off, that is independent of the EEPROM usage in the sketch.

I'm guessing that comment was in the code for a bootloader ?
Then it is about using the EEPROM in the bootloader. Probably no one would use EEPROM in a bootloader, and therefor the functions to access the EEPROM should not be included in the bootloader. What you saw is perhaps the option to include those functions.