A drop kick is legal from anywhere on the field already. (Technically, there's nothing in the rules preventing a place kick from anywhere on the field. Can't see anyone trying it, though.) I don't remember when the last one was (aside from Flutie's), but I do remember Wilkinson attempting one as he was running downfield in the '70s. It's just such a low percentage play, it's not used anymore - kind of like the quick kick (punt on second down). The only case I could see it happening on is what you mentioned, on the last play of a tight game where the ball carrier knows he has no chance of getting to the end zone.
Even similar sports that allow forward passes (e.g. Australian rules, Irish football) restrict how the ball can be launched (e.g. bump with the fist). I'm thinking a straight underhand toss would make it too easy to make the completion, which I think is why the restrictions are there.
As for being onside on a kick, I'd like to see players being able to put themselves back onside by getting behind an onside player, which I think is the rule in rugby.
I'd also like to see the rouge only awarded if the ball is playable, i.e. it hits the ground in bounds or in the goal area. If it flies through the end zone and lands out of bounds, no point. (This isn't exactly what you were looking for, I know, as it makes it slightly closer to what happens in the NFL.)