I think there is a lot of reasons why he was never considered as an icon to people but lets go back and review, look at guys like Rock, Austin, Cena, Andre the Giant, etc. the main reason these guys are relevant because when they were noticed they weren't somebodies lackey, I mean think about it Rocky came to his own joining the nation, but quickly took over because really he was their only champion and Ron Simmons was losing relevance as a leader and heel. Austin may have came in as the ringmaster and then Stone Cold with Ted Dibiase but broke out on his own and made his name with the infamous Austin 3:16.
Hulk Hogan is another prime example, he may have been in the AWA before coming to the WWE, but he was never a champion until he stepped foot in the WWE ring and beat the Iron Shiek to win the title, and from there Hulkamania went wild, Ric Flair was the leader of the four hosemen and never really took a backseat, Andre the 8th wonder of the world who use to wrestle 2-3 men at a time, was the main staple in the heenan family in the mid 80's could never be forgotten just because of his sheer size. And today's era you have John Cena and while they may not have him directly in the limelight he started off wanting to make a name for himself in Kurt Angle, and later doing his rap gimmick and coming into his own as a star...
So lets look at Triple H's legacy Triple H started off as his own guy in Hunter Hearst Helmsley an arrogant snob in a time where goofy gimmicks like the Duke the Dumpster Drose, and The pig Farmer Henry Godwinn ran rampant in WWE. Around the time he found himself as Triple H he was being held down anyways for the infamous final curtain with Razor, Diesel, Kid, etc. when he was finally put down as some importance by being involved in DX but again IMO was shadowed by HBK, Then he took over, but it was the same goof, and was gaining relevance only to then head to the corporation where he wasn't yet relevant as The Rock was the focal point, it wasn't until Trips won the first title that he started really getting momentum and then once the revival of DX and him and Steph took over running Raw did we really see a change, but look at the facts he wasn't really Wrestlemania main event material until Wrestlemania 16 when he still co-main evented with Big Show, Rock, and Foley by that time Austin had main evented twice, Rock was the main heel turned face. Triple H didn't even run a singles main event in WWE until wrestlemania 18 which he only had because he returned from serious injury. so here we are 10 years later from Wrestlemania 18, and since then HHH has been a double digit champion, held every title thinkable, and is now running the show. Is he icon status IMO yes, but its the amount of time it took to show he was on top is why there are many who watched him under a microscope and said he never made it.