The show definitely seemed to center around him more than anyone else at that time, which was rare since he was a heel.
It's also noteworthy that ratings came down quite a bit during this time. The level of nepotism with his character was criminal and I think a lot of fans knew it.
This was Triple H's ascension to the top, for those who like to have amnesia (or are unaware), and forget that he's been doing the Stephanie type of shit, long before Stephanie. None of his rise was EVER through natural means.
*Get yourself in good with Nash & Michaels, who were essentially running the show, by brown-nosing and carrying their bags. Literally.
*Slide your way into Michaels' meetings with Vince, and start telling Vince what to do with top stars (while you're still completely unover in your Hunter Hearst incarnation).
*Start using that position to try to fuck over your competition. [See the note in Bret Hart's book about how HHH tried to use Bret to knock off The Rock, after The Rock was booked to win the IC title from HHH...HHH then tried to use his power to book Bret knocking off The Rock for the IC title, but Bret refused to beat The Rock, because he didn't want to stop The Rock's rise, and saw it exactly for what it was [HHH trying to fuck over The Rock] and this infuriated HHH. The Rock in his book wrote about other wrestlers trying to tear him down, and credits Bret for being generous and looking out for him. He also praises the other big names at the time, with Shawn being the glaring omission.]
*Bret also refers to HHH & Shawn constantly badmouthing The Rock to Vince, claiming that he was stiff, missing spots, etc., etc. You can't write it off as just Bret, since this is the Kliq's M.O. Countless other wrestlers have talked about this being the way the Kliq would knock off wrestlers that they didn't like (Shane Douglas, Vader, etc.), using those same exact words. This was a concerted effort on their part.
*HHH tries to get himself booked into beating Bret cleanly at a house show. Bret is at the top of his game at this point and HHH is...HHH.
*Shawn attributes most of the Montreal stuff to HHH, in both his book, and the Greatest Rivalries
DVD. So we have one of the biggest situations ever in wrestling, with only four people in on it, and making decisions on it...Shawn, Vince, Jerry Brisco and....HHH. Wtf? Who is he? And HHH was the shot-caller! Amazing. And the worst part is, Vince & Bret had already come to an agreement, with Shawn onboard, until HHH talked him out of it (Bret beating Shawn in Canada, and then dropping the belt to him cleanly in Springfield). Regardless of the merits of the Montreal situation, the fact that HHH was even in on a high level discussion like that, is unbelievable. And goes to show you how far he was using his behind the scenes climbing.
*HHH remains on the booking committee, and presumably after Shawn retires due to injury, is the only active wrestler in this position. Coincidence that he would rise into the position that he did, while Austin & Rock attained it through natural means (and The Rock attaining it despite HHH trying to use his positioning to knock him off)?
*Dumps his long-term, live-in, girlfriend, for someone who is the complete polar opposite of her, both physically & personality-wise. Keys to the kingdom set for life.
And suddenly HHH is one of the GOATs...supposedly. And a new generation will claim that "hey, he did it before Stephanie", not understanding that it never happened organically. There was politicking and "Stephanies" long before Stephanie. And that's why anyone who was around back then, can never take HHH seriously, because he did not get over in a natural way, without the behind the scenes usery, unlike Austin, Rock, Hart, and even Michaels' rises. Yeah, Michaels started politicking later on into his career, but he was already quite big and respected, with performances like the Ladder Match. HHH is the only one who's been using, brow-nosing, and politicking from DAY ONE. And it never stopped.
Aside from many other reasons, it's just hard to be considered a GOAT, when you know of all the behind the scenes machinations that had to take place in order to even get into that position. Most others got there through their sheer talent, maybe with just a slight bit of scheming on the side. With HHH, it was a whole hellavu a lot of scheming, plotting, and self-serving bs. From day one.