The security provided by the free Let’s Encrypt certificate is the same in every respect as the security provided by a paid certificate. Connections are not more strongly encrypted when a paid certificate is used.
As you’ve seen, Let’s Encrypt certificates don’t include any information about the legal entity that operates a web site (such as a name, address, or country) because Let’s Encrypt doesn’t have an automated way of finding out that information. Some paid certificates do include that information. However, web browsers don’t directly use that information for any authentication purpose and it doesn’t make the connection more secure at a technical level.
If you have individual users who expect or want to check that information (manually, by going further into the browser interface to look it up), then you’ll need a paid certificate that contains identity information.
There could also be an effect where some users may feel, subjectively, that sites that use more expensive infrastructure are more “legitimate” because they can afford to pay for that infrastructure, even though they don’t need to! So there could be some users who feel that they would rather interact with a site that has a paid certificate because it shows that the site operators have more financial resources available.
In some circumstances, that judgment by users might even be correct!
However, it couldn’t be very common right now for users to think about this this way, especially because many web browsers no longer make the information about certificate issuers or certificate types obviously visible to users. So this information wouldn’t be presented in an obvious way to most Internet users and most Internet users probably wouldn’t understand this distinction easily.
I’m not aware of industry or regulatory rules that would prevent the use of Let’s Encrypt certificates by any type of web site. Maybe we should make a list of major sites that use Let’s Encrypt.