Everyone on the panel touched on some reasons why. Basically from my perspective, having worked at the label mentioned the most in the video...
1. Lack of evolution.
In many ways, NY rap basically boiled down to the same blueprint for well over a decade. You needed street records for the streets, and a poppy rap n bullshyt single for the masses. R&B chick on the hook. The rapper put very little effort in crafting an actual SONG. Often the tracks came as-is, the rapper just needed to add 3 verses and that was that. This birthed a generation of rappers who were melodically challenged and unprepared to deal with any shift in trends. I love Nas, he's my favorite rapper...but in many ways he utterly fails at crafting radio SONGS. The same applies to just about every NY rapper. 50 Cent figured out how to master creating SONGS, and he blew up. Post 50....NY rappers were still trying the rap n bullshyt route but that shyt was basically dead outside of a few outliers, like Empire State Of Mind.
2. 50 Cent
Yes, 50 put his foot on the neck of NY. He starved fellow NY artists. And when he fell off no one was there to take his place. He killed his own career with over saturation of wack, repetitive records and by that time the south had already taken over.
3. Samples
Pretty obvious here but goes back to point 1. NY has been unable to craft music that doesn't rely on sampling, jacking r&b hooks, etc. When was the last time a major NY producer came up? Look at every other major region. They all have HUGE producers today or in the last few years. Metro, Mustard, Kanye, 40, Bo1da, DJ Dahi, etc etc etc. Where's NY's hit maker?
The south is making music that is not only smashing charts, but economically viable. Metro isn't losing publishing money to clear samples. Labels aren't worrying about clearing big samples that make or break songs. They're creating beats from scratch, or from some sounds provided by someone like Frank Dukes. It's an amazing set up...
4. The internet
Blowing up today is more about winning the people than anything else. It doesn't matter what you sound like, if people fukk with you they fukk with you. Kendrick doesn't sound west coast (outside of his slang), Cole doesn't sound sothern, Chance doesn't sound like Chicago, etc. New York hasn't been able to find a rapper like that. So many of their rappers are hell bent on replicating 50 or Hov or Nas instead of giving people what they want.
5. The south and west are playing chess, not checkers
Think about what's going on in LA, Atlanta, and Toronto right now. In LA, TDE has one of (if not the) best engineer in rap. They have an amazingly talented group of in-house producers. They're building studios and sucking up talent, including from outside Cali; when they signed Isiah Rashad, they also signed his producer friends from Tennessee, and they helped craft one of the biggest albums of the year (SZA's CTRL). They're BUILDING for the future.
Atlanta is full of great engineers and producers. Mike Will has an incredibly talented in-house production team that is crafting HIT records. Metro/808 Mafia/etc are doing the same thing. They're constantly signing new producers, constantly getting new guys some studio time, etc. They're building for the future.
OVO is signing producers like crazy. Also song writers (wink wink). 40 is one of the best engineers in rap and he's teaching the squad. They're building for the future.
There's not a single relevant producer in NY that I can think of. Premo, Pete Rock, Statik, etc etc have been remaking the same beats for years. The talent under them isn't breaking out either. There was a time when Alchemist was Premo's assistant, and of course Alch blew up. That's not happening in NY anymore. The scene is stagnant, which means the music is stagnant.
but they were the potential building blocks for the next gen..
