EMT here, and I actually worked for awhile as a school teacher.

I see where you're coming from, but I'd be against your idea as you've outlined it. Teaching well is hard. It's not just parroting facts, it's both convincing kids to pay attention at an intrinsic level (really begging to learn, instead of "do this, or I'll kick your ass to kingdom come" -- if you've spent ten minutes in theatre, you know that winning the hearts and minds is millions of times more effective than the barrel of any gun) coupled with serving up information in ways that they can synthesize their own knowledge. Give me enough bananas and I'll train any monkey to write his ABCs in no time at all, but teaching that same monkey to write poetry takes some serious work.

Similarly, EMS is more than just being band-aid patrol and the Medicare taxi. A huge part of it is knowing your city, and that only comes with time and emotional investment. Another huge part is public health -- not just treating people after the fact, but looking for the things that will get people hurt (maybe the loose rugs in grammy's apartment are a trip hazard, and maybe the sink full of dishes means she's not caring for herself properly -- does she need a social services consult?)

There's room for a public service "gap year" before college, but the jobs should be the kinds of things that require minimal training and minimal life experience in order to provide adequate impact.