As another pointed out, he won his first major title in 1999 from Mankind, which was on a RAW episode. This is a topic most people become gullible in and leads them in misconception. Here's a history lesson that got many, including The Undertaker of all people, to respect Triple H. The Madison Square Garden Incident with Shawn, Hunter, Nash and Hall was where they all broke character and gave their final farewell together. Vince had to punish someone, so he punished Triple H. He couldn't punish Nash or Hall because they left to WCW and he couldn't punish Shawn because he was the "face" of the WWE (the one carrying the company). Stone Cold's 1996 King of the Ring massive push was supposed to go to Triple H, but because he was punished, he had to do jobber duties and etc. Guess what? An average person would complain about it and probably quit, but Triple H kept his mouth closed and continued doing business, which led to huge amounts of respect from most wrestlers and the WWE themselves, which proved to them that Triple H has what it takes to be his own. Some might think this is me rambling irrelevant information, but this is relevant.
From 1999 and onwards, he became one of top heels in the WWE. Many legends have praised Triple H for his passion for the business. Even the WWE knew that Triple H was a total package and had the "it" factor. What else? He has drawing power. He can draw money from merchandise and fans wanting to see him (as a heel, they wanted someone to beat the hell out of him because he was probably the most hated at the time). Would he still have gotten 13 total championships? Yes. Here's something I'm going to throw out, though. Triple H didn't get power because he married Stephanie, he already had power. Most veterans like Shawn Michaels, Undertaker, Triple H and hell, even Edge have power backstage. It's just the fact that some won't use that power and some will. Wrestlers earn their power from the amount of time they've spent in the business or how much work they've put in. Hunter marrying Stephanie is totally irrelevant.