Could've at least checked if the website even allows embedding before embedding it, I found two by randomly clicking around that don't.

Yeah, many links in the embedded blog posts don't work either, presumably because the target website doesn't allow embedding. On mobile I always have to open them in a new tab for them to work.

Some browsers actually block embedded pages. Lots of mozilla based browsers will.

No, it's the website owners setting a specific header (X-Frame-Options to SAMEORIGIN), as it prevents someone else from embedding your website and phishing for user credentials.

No browser prevents that by default, but this tip is found in pretty much every "best practices" hosting tutorial, so it's very common to stumble upon that browser error in the wild.