For example, anyone could use Let’s Encrypt to get a trusted certificate, so what makes this trustworthy? Or why not trust everyone that signs their own certificates with a program like OpenSSL?
There’s some great answers already here, but I want to add a detail fir some context. Like others mentioned, Let’s Encrypt does just the bare minimum of verification. They aren’t really verifying that you are who you say you are, they are verifying you control the website. The reason is due to their goal.
They want as many people as possible using a secure Web protocol, and that requires as many people as possible have a certificate for any websites they run. There is minimal verification of identity, but the benefit of encrypted communications and even that bare minimum id is a huge step up in consumer security from old unprotected protocols.
