Is novelty requirement for PhD restricts the selection of research question? From the answers to this question. We can clearly know that novelty is a basic requirement for a PhD degree.  

Now, consider the following statements:

1) Is Goldbach conjecture true?

2) Is P = NP?

etc., 

All the questions have a lot of attention in that particular field and are not easy to get answers for them. But we cannot say it is impossible to get answers.

Suppose I'm a student and my PhD thesis should be novel. I am highly interested in solving one such question. 

In this case, either my supervisor will forbid me in doing research on such question or there are more chances that I may not get PhD because of the sole reason of novelty.

Hence, to the best of my knowledge, either directly or indirectly, the PhD is narrowing down to the topics of recent origin, relatively easily publishable, less saturated etc., 

Isn't it true that the research question has been influenced by novelty aspect of PhD?
Well, it is slightly unlikely that a novel researcher will solve one of the very fundamental problems in their PhD. 

But whilst working on a solution, you will most probably find different other intersting problems which are unsolved or novel an those can be published and can be the basis of a PhD thesis. 

You will have to convince a supervisor that you 


understood the problem well
have some novel ideas which have not been tried before


and with this you may find someone. But be prepared for an intense discussion. It hppens quite often that a student claims to have a solution for a very fundamental problem and after half an hour of discussion the idea is gone with the wind... A good supervisor wants to avoid such a situation during your PhD.