Because a private CA allows you to create a certificate and nobody else has the ability to create certificates unless you give them the keys or a signing CA. With Let’s Encrypt, you are trusting every major certificate authority to not create a cert on your domain; coupled with DNS poisoning means you would end up on a legit-looking but counterfeit website of yours.
Yea that’s the whole trusting trust thing. You can theoretically set up hour browser to only trust your private CA and not trust any of the publicly trusted CAs. Depends on your threat model I suppose.