с 1999 по 2002 годы

If, apart from nominative and accusative, numeral and substantive must go in the same case
shouldn't be
c 1999 (лет) по 2002 (годам)?.
Unless we understand
с годы 1999 по 2002 ?
However "с 1999 по 2002 годы" is what I see in an exercise.
Thank you.

с одна тысяча девятьсот девяносто девятого года по две тысячи второй год.
или
в годы с 1999-й по 2002-й

I'm not sure the phrase "с 1999 по 2002 годы" is the best way of saying it. I think the concept becomes easier when you actually try to spell it out:

С тысяча девятьсот девяносто девятого [года] по две тысячи второй [год]. So, depending on how busy you are, you can skip either the first "год" or the second "год" or both.

I think the phrase "с 1999 по 2002 годы" can intuitively be attributed to the fact that:
С года Х до года Y проходят годы.

I think a much better version would be: "В годы с 1999 по 2002 ..." = "В годы с 1999-го по 2002-й ..."

Thank you for your wide explanation. I thought I have studied enough the numerals but...
"It's a long way to....".
I see that my mistake was to put cardinal numbers where ordinal must fit.
Thank you both.