The problem with epinephrine is that it must be immediately available not just to family members, but to kids, themselves, and teachers, and dealing with components as opposed to just pulling an EpiPen out of a lunchbox will be fatal to any number of the former, and syringes, needles, and drugs placed in schools for use by the latter are guaranteed to get stolen and possibly probably even result in some curiosity-related ODs.
Your concerns are to the point. My work-around would only be useful in limited circumstances.
Another downside — at least in some parts of the USA (and probably Canada) — is, as I've been given to understand, that there might be significant liability associated with the dispensing of epinephrine and paraphernalia.
