I've been watching Fullmetal Alchemist: Brotherhood lately and got to the episode where Ed and Al deliberately try to lure out Scar for their own purposes (I'm trying to be spoiler-free here).
Anyway, I noticed that the townspeople of Central City are all rather astonished that an alchemist would be kind enough to restore their broken stuff to them. The same thing happened in Liore, when Al fixed the broken radio.
It got me thinking: wouldn't alchemists be the best handymen and fixits? All they'd have to do is draw the circle runes and, well, clap their hands. I can understand having tradespeople and mechanics -- those are rather beyond alchemy -- but basic fixings would be well within the realm of an alchemist. Heck, even being a basic production house (making forks and spoons, for example) would be fairly lucrative.
So: do all alchemists end up joining the military in some capacity? If not, do we ever see alchemists engaged in trade?