Let's Encrypt doesn't ever possess your private keys, doesn't know who connects to your site if you use OCSP stapling, and doesn't control what kind of cryptography you use when negotiating TLS sessions with your site visitors. Let's Encrypt also doesn't need any contact information from you when you obtain a certificate.
Let's Encrypt certificates aren't trusted by Chrome without a proof of inclusion in public Certificate Transparency logs, so all issued certificates have to be disclosed.
As I've said in a number of HN comments, the people working on Let's Encrypt generally still think that the CA system is too powerful, and are happy for your suggestions about how about it can made more transparent and less powerful.