I think the answer you are looking for is less privacy oriented than OP understands it to be.
The benefit of renting computational resources someplace outside your control is e.g. that it allows you to send mails to known providers which otherwise would refuse your mail if you would sent them originatig from a private IP address or e.g. having a always on cloud storage without running a computer in your basement 24/7 etc.
I think the answer you are looking for is less privacy oriented than OP understands it to be. The benefit of renting computational resources someplace outside your control is e.g. that it allows you to send mails to known providers which otherwise would refuse your mail if you would sent them originatig from a private IP address or e.g. having a always on cloud storage without running a computer in your basement 24/7 etc.