OG Nick Fury wasn't exactly UN-cool, but he played his concept out somewhat fast as he settled into his ultimate role as a supporting character for the Marvel Universe. His age and history also meant he got tied down as a guy whose heyday was from the past without, say, the youthfulness Captain America had being on literal ice. In addition to the Jackson-ification that simply made him look badass, I think the Black Fury hasn't had to suffer the WW2 connection and so he can grow up as a proper peer to the Marvel U heroes. That lets him do cool stuff EQUAL to the heroes "in the present", which helps a lot.
Finally, as far as I can tell, they did NO disrespect to OG Nick as they more or less retired him, helped alongside it being logical in-universe. He's an old guy, here's his successor (typical convoluted comics origins aside), we can bring out OG for a cool story if we feel like it while letting the new guy shine as the main one. Which also leads to the fact that New Nick is unapologetically still doing the cool superspy stuff, just actually modernized, as well. There's no apologies for the concept, no sense of replacement. A logical, actual reason to modernize the concept occurred and done so respectfully and intelligently without disrespecting the OG character. Far as I know they haven't tried to shift OG Nick's supporting cast personal to HIM onto New Nick as well, but instead let him build his own crew, which also helps a ton.
It vaguely reminds me of how everyone praised the Kingpin being played by a Black man in Affleck's Daredevil - but in that case, I think it's a different concept, where the dude legitimately could and did match him in physicality and personality outside of skin color, which made it easy to drop the issue. In this day and age that's likely too sensitive/culture wars-esque to do, but it WOULD be an interesting exercise to have say Hal Jordan and John Stewart in a live-action film be respectively played by a Black and White dude, while looking as visually humanly close to them as possible, and of course completely matching their respective personalities in acting. Especially since Green Lantern always had people of all colors in its ranks, much less the whole different alien species thing.... but they're all united in being cops and thus ideology (smash criminals).