Does the repetition serve to ensure that everyone present has fulfilled the mitzvah of tefila? If so, does saying "amen" to all of the blessings work in substitution of the silent Shemoneh Esrei, in a time of pressing need? Why do we repeat the Shemoneh Esrei out loud?
Yes, the original purpose was so that if someone doesn't know how to pray, they could hear the chazzan's repetition and fulfill their obligation that way. (Bear in mind that in Talmudic times, knowing how to pray meant a lot of memorization - written siddurim didn't appear until the 9th century.)
It doesn't work for a person who does know how to pray on his own. Also, it requires the presence of a minyan (Mishnah Berurah 124:1). That second point means that it's hard to conceive of a case of "pressing need" where a person who knows how to pray would need to use the chazzan's repetition to fulfill his obligation - he'll have to be in shul anyway, and may as well recite Shemoneh Esrei himself.
Even when everyone in shul knows how to pray, though, the Sages' enactment - of first reciting Shemoneh Esrei silently and then the chazzan repeating it out loud - still remains in effect, just in case it happens one time that an unlearned person shows up. (Mishnah Berurah ibid. :12)
Historically, there was a time when the Rambam ruled (Teshuvos Harambam, ed. Mekitzei Nirdamim, nos. 35-36) that the silent Shemoneh Esrei should be skipped, and they should just go straight to the chazzan's repetition. The reason was because people were talking or otherwise not paying attention during the repetition. There has been some discussion about the parameters of this ruling, though the consensus seems to be that it was only for that particular time and place (see the teshuvah of R' Ovadiah Yosef here).