I would give this to Shawn Michales also after all he is the 1st guy ever to win the Rumble after entering at #1 and he has won 2 rumbles
You have to remember that when HBK entered #1 and managed to win the RR had cut the time between entrants in half, down from 2 minutes to 1 minute. HBK wrestled almost 20 minutes less than Flair did winning when he entered #3.
That tidbit of obscure trivia aside, HBK isnt "Mr WrestleMania" because he won all the time. He did have some pretty big victories there, most notably the Iron Man Match vs Brett Hart & Win Or Retire Match vs Flair, but win or lose HBK always put on a great show, his matches were almost always among the most hyped and talked about matches at the event regardless if it was Main Event or Undercard, HBK wasnt "Mr WrestleMania" as much as he was "The Show Stealer".
Even in a losing effort, HBK was often in the biggest match of the card and delivered a sterling performance (vs Austin, The Three Way Dance for The Title, twice vs Taker, etc). He had some great moments in victory but win or lose he always delivered a "Show Stopping" match.
The only one who I think in WrestleMania history who really comes close to HBK here is Randy Savage, he easily pulled out the greatest match Ultimate Warrior ever had, gave Hogan probably one of the Top 3 or 4 best matches he ever had, put on absolute classics vs Steamboat & Flair, and his initial title win vs DiBiase was very good. Win or lose, Savage routinley stole the show with his performance, main event or undercard, and his match was always among the most talked about and most important on the card. Some people will argue that having a great match vs Steamboat or Flair back then isnt a challenge but what he did to elevate Warrior in their bout as legit performer was unreal. People give Flair credit for making average performers like Lex Luger look great, Luger looks like Kurt Angle compared to Ultimate Warrior.
You also have to include Undertaker in the conversation. Even though his streak wasnt a big deal until around WrestleMania 17 & 18, twenty straight years without a loss is huge at one event, and certainly in recent years his matches have been at or near the top of the card pretty much every year since WM 17. Triple H, HBK, Flair, Batista, Edge, he's had some big time matches in the last ten years to keep the streak alive and just as important has delivered very good to great performances every time.
As for Kane, it's hard to call him "Mr Royal Rumble" when he has never won. If he had maybe two victories under his belt alongside his impressive numbers for eliminations, etc, then maybe he would worthy of that monicker. It's like great quarterbacks, you have to actually win a couple times to really be in the conversation for greatest all time. People may debate Unitas vs Montana vs Elway vs Brady but they never add Drew Bledsoe, Dave Krieg, or Boomer Esiason in the conversation. They were all successful, pro bowl caliber players, but they didnt have the post season wins and hardware the other guys have.