the Cert just confirms, that the domain your accessing is belonging to who owns it. When you signup for a cert at LetsEncrypt, you have to run a script on the source, which confirms as your domain.
You wouldn't be able to get a Cert for e.g. amazon.com - because you wouldn't be able to run that specific script on the source and so LetsEncrypt couldn't confirm if that domain really is yours or not. And that's as well the reason, why not trust everyone,