How to delete purchase history on Apple ID

No. I'm saying you can hide items from a re-download list using a computer but not hide or delete a purchase history.

Here is seeing your purchase history: See your purchase history in the iTunes Store on a Mac or PC - http://support.apple.com/HT204088

Here is seeing a re-download list: Redownload apps, music, movies, TV shows, and books from the iTunes Store, iBooks Store, and App Store - https://support.apple.com/HT201272

Apple does not say why this is not possible. If it were me setting this up I too would prohibit it because I wouldn't want all the emails from people who 3 years later decide they do want something after all and then say Apple is "stealing" from them by not letting them have access to their purchases.

if you don't like it then tell Apple:

http://www.apple.com/feedback/itunesapp.html

Is there a legal reason why the 'purchase history' cannot be deleted?

I have a similar issue to this in that I want to delete a couple of items from the history.

The books in question were free to download therefore technically and legally (maybe) not purchased.

The definition of 'Purchase' (in most of the accepted dictionaries) relates to buying something and the definition of 'Buy' is to exchange goods or services for money. As no money (and nothing with a monetary value) has changed hands the books were not actually purchased. Are Apple overstepping the mark in not allowing the deletion of information relating to 'non-purchased' items?

This hasn’t answered the question as to why we are unable to delete our own purchase history? I don’t just want to hide it. I want it gone. How can I do this?

You cannot. You can hide items from your redownload list but your purchase history cannot be modified.

Hide and unhide music, movies, TV shows, audiobooks, and books - https://support.apple.com/HT208167 - "Hiding an item doesn't hide the record of purchase." It will still appear in your purchase history. Has to be done on a computer through iTunes.