Consider the BBWAA Hall of Famers since 1983, the last quarter-century, and their path to induction:
First five years: Juan Marichal, Brooks Robinson, Harmon Killebrew, Lou Brock, Willie McCovey, Catfish Hunter, Willie Stargell, Carl Yastrzemski, Johnny Bench, Jim Palmer, Joe Morgan, Gaylord Perry, Ferguson Jenkins, Rod Carew, Tom Seaver, Rollie Fingers, Reggie Jackson, Steve Carlton, Mike Schmidt, Phil Niekro, Don Sutton, Robin Yount, Nolan Ryan, George Brett, Carlton Fisk, Dave Winfield, Kirby Puckett, Ozzie Smith, Eddie Murray, Paul Molitor, Dennis Eckersley, Ryne Sandberg, Wade Boggs, Cal Ripken Jr. and Tony Gwynn
After: Don Drysdale, Luis Aparicio, Hoyt Wilhelm, Billy Williams, Tony Perez, Gary Carter, Bruce Sutter and Rich Gossage
The vast majority of primary-path Hall of Famers in the modern era spend five or fewer years on the ballot. That's not to say that BBWAA doesn't make mistakes of commission in that time, but having a 15-year window isn't adding a whole lot to the process. Of the players in the second group, you have some of the weakest and most controversial BBWAA Hall of Famers, and not coincidentally, those are the ones who were on the ballot the longest. If you're not voted in on the first... let's raise the bar from five to seven ballots, which is a dozen years after retirement... you're probably not raising the standards. So cut off the eligibility then, make it a five-year, or even a three-year, waiting period, and a seven-year eligibility window. Look at the above lists, and tell me whether a 20-year window is allowing for an evaluation of a career, or just for mythologies to form, with the players becoming pawns in the modern arguments about observation versus data in career evaluation.