for me, at the 12u level at least, I wouldn't want to add when to throw to first base from left field and when not to throw it to my left fielders mental responsibilties. Or centerfielder either. It surely wouldn't be when there is another runner moving from 2nd to 3rd as the original post stated.
Being aggressive is great. Most aren't aggressive enough. However there is a limit to how aggressive you want them to be. Being overly aggressive will eventually lead to mistakes. Some caused by when the other team realizes you're being overly aggressive and they'll bait you into making those mistakes. Just don't see the sense in making a play from mid depth left field to first base on the batter, especially with runners on. If its a close game you're taking a big chance if it doesn;t go well. If you're winning in a blowout and there is no harm by giving up that run if something goes wrong with the throw from left to first, then why embarrass the slow runner. To show off Mary's cannon in left? If so, Mary's not really showing off her arm. Instead she is highlighting that something is wrong with the runner. Because there is not a player out there that can throw out a normal, uninjured, player at first base from normal mid depth left field. Center also. If you're losing in a blowout, just go by the book and make the traditional fundamental plays. Don't look to make things worse by trying to make a play that shouldn't be attempted in the first place. This may work in the younger years, but as they get older, the chance of throwing a girl out at first from left or center field on a routine single goes down to none. Barring her falling down on the way to first or something like that.
Though I will agree, that if it happened to one of our runners, I'b be wondering how it did and what is wrong with our runner.