@strontium it happens here in Australia too, and personally I think it’s better that way. However I think it depends on the country. The Australian, American and Canadian anthems are all songs that are very specifically about the country. I mean, any monarchy could have God Save the Queen/King as the anthem, it’s not very specific to the country. But if any country other than Australia, America or Canada had “Advance Australia Fair”, “O Canada” or “The Star Spangled Banner” as anthems it would obviously be silly (although in the latter, the USA is never actually specifically mentioned).
Basically what I’m trying to say is that, in my mind, the lyrics in the above anthems are much more significant and specific to the country than in the British anthem.