"One thousand, two thousand, three thousand."
Translation:אלף, אלפיים, שלושת אלפים.
The construct state of numbers wasn't originally used only for definite things (it's not uncommon to see in the Bible things like "שלושת ימים" which in modern Hebrew would be "שלושה ימים").
It's also still used in the number two, like "two houses" = "שני בתים" and not "שניים בתים"; and in other numbers, not just thousands, like "שלוש מאות" (three hundred: shlosh me'ot and not shalosh me'ot).
Not at all, I think that's a good question. I think radagastthebrown's answer sums it up, there are no other exception in modern Hebrew, at least not that I can think of now. There is שני/שתי, there is numbers of מאות and numbers of אלפים, that's it. Not even other numbers such as millions - שלושה מיליון.