I’m one who says “twenty oh four”, but then again I’m a reckless iconoclast. Few people in my area say it that way. I’ll also sheepishly admit that I called 2000 “two thousand” and not “twenty hundred” as I should have for perfect consistency.
But, starting in 2001 I switched to the “twenty” convention that I’d already decided in advance I would use, public opinion be damned.
My bet is that come the year 2020, people will find the temptation to say “twenty twenty” too great to resist, and the proper convention will be restored. Just you wait.
I have read a number of “old soldier” memoirs of the Napoleonic Wars, and they frequently use “the year 0”, “the year 1”, etc. for 1800, 1801, and so on. This would be one way to avoid the issue (or confuse it further).
I’ve a horrible feeling we Anglo-Hibernians (or Hiberno-English, so as not to offend the bogtrotters) will actually resort to saying stuff like “two thousand and seventeen”, which is seven syllables and is a complete waste of energy.
Now, while I agree that people probably will say twenty twenty-one, your two examples are more extreme than this case. Note:
Ten sixty-six versus One thousand sixty-six - difference of two syllables Twenty-five twenty-five versus Two thousand five hundred twenty-five - difference of three syllables Twenty twenty-one versus Two thousand twenty-one - difference of one syllable