Blame spans from Little League to lacrosse to Dennis Eckersly. For those who cite old-timey hardball -- when kids played every day all summer (and not in uniform, especially not ruled by adults), pitcher really was an actual position; not a subgroup of the roster. One guy on the neighborhood team played shortstop, another was catcher, and one guy was always the pitcher. Imagine the stamina of those hurlers who made it to the pros...
Nowadays with so many other interests vying for kids' time (including lacrosse as a direct conflict in the spring), young arms are throwing less than ever. That includes Little League, where there are now strict weekly limitations (either number of batters or innings), purportedly to protect shoulders and elbows -- but also, so cut-throat coaches don't use a stud to dominate competition. In the leagues my son has played the past few years, managers rotate every child on their rosters around the diamond, including the mound (which is great for spectators who love walkathons, and for outfielders who collect dandelions).
MLB changed big time with the success of Eck, the first automatic one-inning closer. Just about every other club has been seeking to replicate the virtual improbable ever since (except for the Rivera Yankees); like today's shifts, openers and other copy cat trends. Before the 9th inning man, relief aces were workhorses, regularly throwing over 100 frames, with lots of two, three or more inning stints... like when ex-Red Sox Sparky Lyle led the Yankees in IP in winning the last two games of the 1976 ALCS.