If Trips hadn't gotten injured, I think a lot of 2001 would pretty much remain the same.
Jericho & Benoit would've still won the Tag Titles from Austin & HHH on RAW, which would've lead to a rematch at King Of The Ring but with the WWF Championship on the line also. Or we might've seen a Fatal 4 Way for the WWF Championship, or Benoit-Austin for the title in the main event & HHH-Jericho in the co-main event. Either scenario, Austin would've stayed the WWF Champion.
Then in the Invasion storyline, we could've seen one of these two options.
HHH in the same role that Angle played, where he & Team WWF are betrayed by Austin in the Inaugral Brawl at Invasion, Trips goes onto face Austin for the WWF Title at Summerslam & Unforgiven, and he wins the belt at Unforgiven before he loses it back to Austin on RAW, then Trips joins the Alliance as a mole and costs the Alliance the match at Survivor Series, ending them once & for all
Or, both Triple H & Austin join the Alliance, leading them together while Angle & The Rock lead Team WWF. In the last few months before Survivor Series, we see Triple H & Austin secretely plotting against each other to take over the Alliance, which results in HHH leaving or getting kicked out (yes, even by Stephanie) & he rejoins Team WWF, or HHH gets so sick & fed up of Austin by Survivor Series, that he betrays him & the Alliance in the match, ending them once & for all
So either way, I think HHH would've been the man to end the Alliance. I dunno if he still would've went on to win the Royal Rumble match but with him being a huge face because of him ending the Alliance, I'd like to think that maybe he still would've. Actually it depends on which scenario would've happened
If it was the second then I could see HHH still winning the Royal Rumble match and winning the Undisputed Championship at WM since he wouldn't have won it if he & Austin were leading the Alliance.
If the first option, then I think The Rock would've won the Rumble match and won the title at WM since he had come back but not yet won the WWF Title. And HHH probably would've brought HBK back early to face the nWo at WM (against Nash & Hall, if Austin agreed to face Hogan but if not, then 2 on 3).