You have a slight issue in that you are referring to archetypes by their lanes. Currently, multiple archetypes (Mage, Tank, Fighter, Assassin) can easily all fit the positions of top, mid, and jungle. Support and Marksman can also do this, rarely, namely Vayne, Teemo, Quinn, Kayle, and Lulu. Marksman Bot lane with an at least partial support seems to be the only constant.
Back in the days of beta, there was absolutely no meta of what characters went where that was set in stone. Characters were only created with archetypes in mind, not positions. Hell, jungle wasn't even considered a standard position until it was popularized in tournaments.
To answer your question, Blitzcrank was created to play like Pudge from DotA, a tanky brawler that made picks to start teamfights. He wasn't even considered to fit the support archetype until the bot lane adc support meta emerged in season one.
You already knew the answer to what blitz was, but just didn't quite understand how the meta has evolved into what it is today, rather than being the end all be all since the advent of League.
Bonus: In the days of Alpha, riot shifted between Summoners Rift holding 6 champions to 4 champions, the idea of top lane solo and bottom lane duo came from the days of 4v4 rift, because bot lane had better control over dragon in the early game. Jungle as a role was not introduced as even possible until either fiddlesticks, master yi, or warwick was created. They were the first three champions even CAPABLE of the role throughout beta.
