They're paying more-or-less Harper money for a player of similar age but who has Harper's one peak year almost every year. Trout is #1 on the all time bb-ref WAR list through his age. You can go down 50 or 75 spots below Trout and you have 80% of the players there as clear HOFers.
Trout's peers are Cobb, Mantle, Hornsby, ARod, Foxx, Ott, Griffey Jr, Speaker, Vaughn, Aaron, Frank... If you're not willing to pay going rates for Mike Trout, you would have also been willing to let any of those players walk because they were too risky.
Here's a list of players whose entire careers were worth less than Trout has been so far: Winfield, Ashburn, Billy Williams, Sliding Billy Hamilton, Lou Boudreau, Home Run Baker, Jesse Burkett, Harmon Killebrew, Mike Piazza, Vlad, Yogi, Hank Greenberg, Willie Stargell, Bill Dickey, Joe Medwick, Willie Keeler, George Sisler, Jimmy Collins, Elmer Flick. There are nine Hall of Famers whose entire careers were worth less than half of Mike Trout's first eight seasons.
I agree with you that Beane and Moneyball was really influential...but it only sorta', kinda' worked.
Hudson 238 IP ERA+145
Zito 229 IP ERA+ 158
Mulder 207 IP ERA+125
Lidle 192IP ERA+112
Zito and Mulder were first round draft picks. I didn't read the book, but I loved the movie. But I think the truth is that analytics had way, way, way less to do with the success of those teams than the hype would lead some to believe. If so, then the influence of the book on the spread of analytics may be more to do with hype and spin than an actual analysis of the effects of analytics. I find that fun. It will be interesting to see how analytics are viewed in ten to fifteen years. I think in some cases the "success" of analytics on team wins could be luck much like how some scouts back in the day made a name for themselves by signing a player that turned out to be a great player. A big part of that is getting lucky with injuries, etc. I wonder if the same thing might be happening with some of the models that supposedly said pick player A over player B in a draft, etc. Only time will tell and maybe not even then (pretty soon everybody will be doing pretty much the same thing with analytics and there may be no relative advantages as it becomes part of the status quo).