"Visually identical" is never good enough. Have you heard of attacks confusing Latin letters and Cyrillic letters? For example C versus С. (The latter is known as CYRILLIC CAPITAL LETTER ES.) Have you heard of NFC forms versus NFD forms? For example é versus é (LATIN SMALL LETTER E + COMBINING ACUTE ACCENT versus LATIN SMALL LETTER E WITH ACUTE.)

Nothing that's important when it comes to security and privacy should rely on a "visually identical" check. Fortunately browsers these days are already good at this; their address bars use puny code for the domain and percent encoding for the rest of the URL.