> I find interesting that HBO, a US TV network, has become a worldwide brand name in a way that CBS,[1] NBC, and ABC didn't;

That's because CBS, NBC and ABC are national broadcast networks while HBO is a cable network, like CNN. CNN is broadcast internationlly.

> only BBC has also transcended its home country this way,

That's only because of the british empire. Who but their former slave colonies watches BBC?

> None except Netflix has yet gained worldwide recognition for their shows and brands, yet, though (not even Disney and The Mandalorian).

Isn't Friends the most popular tv show worldwide? People may watch it on Netflix but it was originally broadcast on NBC as part of the "Must see tv" thursdays.