Five tries later, I have yet to finish "The Dark Knight"

No, I don't believe that any Director's work over the past quarter century represent the era. I would suggest that there are Director's whose work over that time period stand out to the same degree, generally, of the work of Directors in past eras.

Directors with the most films in the 21st Century list:

8
Joel Coen & Ethan Coen
Richard Linklater

7
Christopher Nolan
Martin Scorsese,
Steven Soderbergh,
Steven Spielberg,
Quentin Tarantino.

6
Pedro Almodóvar,
Wes Anderson
Olivier Assayas,
Claire Denis,
Michael Haneke,
Jia Zhangke,
Guy Maddin,
Apichatpong Weerasethakul.

5
Noah Baumbach,
Nuri Bilge Ceylan,
David Cronenberg,
Jean-Pierre Dardenne & Luc Dardenne,
Clint Eastwood,
David Fincher,
Jean-Luc Godard,
Alejandro González Iñárritu,
Paul Greengrass,
Werner Herzog,
Hou Hsiao-hsien,
Spike Lee,
Mike Leigh,
Jafar Panahi,
Park Chan-wook,
Tsai Ming-liang,
Gus Van Sant,
Lars von Trier,
Frederick Wiseman

*PT Anderson directed 4 and all are in the top 1000. And you will find in this LINK that his reputation stands out in the 21st Century.

So I do feel that it is valid to pose the question I did.

 

Why don't you just give up?