Hi, when we crop page inside PDF documents, all content outside the cropping area remains in the document and you can access it in Illustrator.
Other basic apps provide the option to completely erase what is outside the cropping area (see https://www.easepdf.com/crop-pdf/). Such a simple tool should be avaialble in the cropping dialogue window in the form of an option to tick for those who do not need to keep this content.
And please, do not tell me about optimization and other editing tools: it should be there, right there, when you crop a document, without having to dig deep inside the app and discussion forum to eventually understand that the Redact tool which could eventually help you get rid of this content just... does not work in most cases!