EMTs are not the target customer of epipens. They work with life-threatening situations day after day. To a kindergarten teacher, if a child if having an anaphylactic chock, this is very far from a "very slight increase in complexity".
Just to ground the situation, the kindergarten teachers at my daughters place are already freaked out from the thought of having to administer an epipen. I can't even start to imagine how they would handle a syringe and a bottle.
There are thousands of people out there who carry IM Glucagon kits, an similarly time sensitive medication, intended to be administered by untrained bystanders. If it works for Glucagon, I see no reason it can't work for Epinephrine. In reality, there's no need for a vial, the syringe can be prefilled with the correct dose.
Just to ground the situation, the kindergarten teachers at my daughters place are already freaked out from the thought of having to administer an epipen. I can't even start to imagine how they would handle a syringe and a bottle.