The phrase "universal importance" is correct and can be used in written English.
It is typically used to refer to something that is important to everyone or has significance on a global scale. Example: The issue of climate change is of universal importance, as its effects are felt by every nation and could have devastating consequences for the entire world.
America is an imperium, and what goes on within it has a universal importance.
Not one interviewer asked about the universal importance of political freedom.
It is of universal importance that a deal is struck that is ambitious and achievable.
Discovering the Universal Importance of Plasmas at RLE Research in RLE's Plasma Physics Group.
The universal importance of emotion to artistic expression was central to the debate at the Royal Society.
Ion channels are of universal importance for all cell types and play key roles in cellular physiology and pathology.
It is considered that the results in the present are of universal technical importance both in designing solar cells and their surface structures.
The discrediting of one should not mean the discrediting of the other: I am with Luce in regarding western liberalism's values – from respect for human rights to the protection of freedom by representative government – as of universal, paramount importance.
(A recent newspaper poll in Spain found "One Hundred Years of Solitude" ranked just after the Bible and "Don Quixote" in universal historical importance -- surely the voters can't all have read it?) Indeed, it is hard to conceive what our sense of the novel, or even of Latin America itself, would be like now had the writings of Gabriel García Márquez never existed.
He liked to think of Wagner's works as Greek tragedies, of fresh and universal human importance.Nonetheless, because the Nazis had commandeered them, and because most of the family had been only too happy to go along, there was much purifying to be done.
Population systems have long been an important theme in mathematical biology due to their universal existence and importance.
