[Sethomas]

See, that's actually a really fun question and there are amazingly elaborate/bizarre answers (cf. Anselm of Canterbury's Cur Deus Homo) and and lots and lots of painfully boring ones (cf. anything written by John Calvin).

The convention answers are all centered around the idea that God offered Jesus as a sacrifice (to whom... the GODS??) in order to atone for mankind's falling. Jesus' death was never intended to be taken as a free pass to heaven for all humanity just because it happened, it was taken as like a gesture to legitimize man's quest for salvation in earnest. Simply put, man is so depraved in his natural state--BC or AD--that he can never DESERVE heaven. Jesus' death did not "remove" original sin per se (it's often simplified as saying it that way, so I'm not calling you out on saying it "wrong"), he merely came in to establish that original sin was no longer an end-all conclusion that bars people from eternal salvation. Hence, it's worth noting that the Old Testament Jewish culture sometimes referenced an afterlife, but in general it's clear that Judaism up to Jesus did not believe in an afterlife at all for the most part.

Convention: original sin says that everyone goes to hell. Jesus dying makes it not quite that bad; now you can work really hard and maybe not go to hell.

Okay! So, here's my take on it:
The early Jesus movement, known to us by literature written in the period from 10-70 years after his death, all has this overbearing theme that Jesus dying was a necessity for human salvation. Every age since then has taken it upon themselves explain what the hell that actually means and why.
It was Jesus' responsibility to take a few grains of truth from the classical, pre-Rabbinical Jewish religion and mold them into something that would better suit a more advanced, sociologically adept civilization. Genesis was written for rubes walking around aimlessly in the desert, Revelations was written for a fledgling movement being oppressed by a mighty formal empire.

The historical implausibility of the Jesus movement cannot be overstated and nobody's stating it. The secular camp doesn't say it because it seems to legitimize a historical person as being a theological image, and the religious camp doesn't say it because it calls his divinity into a scrutinized light that makes them uncomfortable. To culminate roughly seventy years of militaristic messianic expectation, to look no further than anti-Roman apocalyptic fervor, with the message "render unto Caesar what is Caesar's" and "turn the other cheek" is the most baffling historical fluke possible.

The Gospels were written with the agenda of making the Jewish authorities look bad regarding Jesus' death (to call them anti-Semitic in this historical framework is non sequitur) but his actual death would have been completely nonchalant for the perpetrating Romans and a tipid roll of the eyes for mainstream Judaism. But the fact that Jesus as a historical character literally threw himself to death on a cross just so that people would take him seriously with a message that nobody on earth wanted to hear... that to me is absolutely amazing in a purely historical framework. It was literally the best PR move in history.

To me, you can kind of put that together into this idea that Jesus died senselessly with the goal in mind that people would take his message seriously.