Actually the trend was started by South Africa in the the 90s (as early as they were allowed to play international cricket). But they were kind of proper batsmen/alrounders who were pretty decent with bat (Pat Symcox, Nicky Boje, Klusener, Pollock) The idea was to make it look (to the opposition) a lengthened batting lineup and plan the innings accordingly, with controlled aggression and not necessarily pinch hitting for some overs.
However it is definitely Jayasuriya/Kaluvitharana who astonished this what we call pinch-hitting (for players who are supposed to be pure batsmen!) I think the concept of pinch-hitters (who are basically tailenders with some slogging skills) came into existence even before Jayasuriya/Kaluvitharana! But I can also remember somebody like Kris Srikanth who used to do something similar to Jayasuriya in first 15 overs in 80s itself!
But definitely the trend has changed now! We expect the openers themselves to do this role (with support of No.3 and even No.4) in addition to building innings! Their job is made easier with batting-friendly conditions and rules!
You can relate this scenario somewhat to our current Indian movies as well! In the past, we were seeing specialized girls for cabaret dance/songs and heroines were kept decent! But now the heroines themselves do all the roles