Put all of that on the client, do your best to protect it but ultimately make it the clients responsibility.
I still haven't seen any lawsuits or regulation targeting software in that sense, apart from DRM.
This is again the difference between engineer vs policymaker.
As far as I understand it, Microsoft has no responsibility for PIIs e-mails going through the Outlook e-mail client. Maybe the US is different, but at least in Europe, the GDPR is clear that software vendors have no responsibility in data being processed locally when it's deployed and run by others.
Oracle has no liability for the data stored in their database.
If you have no way of touching the data, your servers (self-managed or otherwise) aren't touching data in any form, you have no legal liabilities wrt data (apart from agreements of course).
Or am I missing something?
Wrong. HIPAA applies to any business that transmits and/or has access to PHI. You don't need to be storing data on your own hard drives to be subject to these laws.
This is exactly my point. You are thinking like an engineer, and Congress is not. You cannot assume anything. You need to hire a lawyer, or you are opening yourself up to serious liability.