NXT Executive Producer and Founder Triple H
While Triple H already has a ton of work on his plate, having the actual boss of NXT serve as the GM would bring more authenticity to the brand.
NXT is what it is today because of Triple H. In its original format, NXT was seen as a sort of joke by many pro-wrestling fans, but Triple H has made the brand a place where performers can show their talent and get ready for RAW or SmackDown.
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Somewhere along the way, Triple H began bringing in wrestlers that were huge on the indies, like Johnny Gargano, Tommaso Ciampa, and Bayley. These acquisitions (and countless others) made NXT a viable place for fantastic pro-wrestling.
In 2011, Triple H relieved Vince McMahon of his duties in storyline and became COO of the WWE. This storyline gave WWE fans many memorable moments, such as a great feud with CM Punk, the roster going on strike, and a feud with Brock Lesnar.
It also led to Triple H and Stephanie McMahon's The Authority storyline. Triple H coming in as NXT GM would make the brand seem more realistic, as the actual boss would be controlling the brand on air.
Triple H loves NXT and is very passionate about it, and that would translate on screen.