If one purpose of the repetition of the Amida is to allow those who are not expert in prayer to be exempted of their obligation to pray (as per the Shulchan Aruch, O"C 124:1) why isn't this same device allowable in the absence of a minyan?
Certainly in this non-minyan repetition, anything considered one of the devarim shebikedusha like the Kedusha or the Birchat Kohanim might not be included, but those would be similarly absent from an individual's silent prayer, which the repetition is standing in for. The Amida seems to exist on its own as an obligation and if this repetition is a method by which an unlearned person can fulfill that obligation, why would it need a quorum to be performed?
One might even wonder if the repetition is necessary, or whether an individual can say his "silent" Amida out loud in the presence of one who does not know how and whether this transcends modeling/chinuch and can be motzi the listener though I sense that this might be broached in Tosafot, I just don't fully understand it.
I understand that this question is predicated on isolating this one role/function of the repetition and not thinking of it as a vehicle for the kedusha, or as a separate Tefillat HaTzibbur b'Tzibbur, but as, it seems, this service on behalf of the unlearned was the original purpose, would it have been allowable then to repeat without a minyan for the sake of any (even) one present who needed the help?