Why do email providers keep copies of emails even after you delete them?

I set up my iphone with email for the very first time and linked it with my hotmail account. I wasn't sure what all the settings were for and selected one that said something like 'download all email' . I thought it meant it would download all the old emails i have saved in my inbox.

It actually downloaded every single email i'd ever sent or received since i opened the account way back in 2003. If i deleted the emails, then how could the iphone have restored them? I was able to click on emails 10 years old and read them!

How is not a privacy violation for them to have kept all my deleted emails?! Why are they saving them all?

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