The banner is required every time there is processing of personal data where consent of required, whether that processing happened thanks to cookies or thanks to any other technical means (1px gifs, JavaScript fingerprinting, etc)
Most websites do not need to process personal data (typically for analytics reasons); it's perfectly fine to run without that and only use personal data for transactional reasons, which AIUI doesn't require that sort of consent.
The banner is required every time there is processing of personal data where consent of required, whether that processing happened thanks to cookies or thanks to any other technical means (1px gifs, JavaScript fingerprinting, etc)