It only saves the problems if you can maintain the same level of availability and integrity, what happen when you have an outage, when your hard drive die or when your house burns? What if you forgot to encrypt your data and your drive gets stolen? Can you patch your server vulnerabilities faster than company x ? What about simple maintenance like certificates renewal? It's not that easy to be better than a tech company.

Regarding pure privacy, it's getting better with new regulations like GDPR, but yes, the best is to not share data with third parties.