Is this kid illegitimate ?

Nikah is requirement for having sexual contact with free women(hasanaat) , there is no requirement for nikah to have sexual contact with a slave woman.
Does Islam consider those child which are born out of wedlock to a slave woman legitimate or not ? There is no wedlock in this case , is it ?
So your nikah theory for a child to be legit goes out of the window.
Now the second part there are many kids which are born after the father has died , so your theory of a father physically and financially contributing for a child's upbringing also goes out the window.
Dear Sir. Quran and Hadees are flawless they do not have the kind of flaws a human theory and ijtehad will have. That is why I asked for references from Quran and Hadees.
Personaly I have no stance at this point on this issue. I am trying to understand and learn myself this new concept in this day and age. So please do not take my comments personal .