Arcane force itself is a kind of prequest to training maps and end game bossing, a really long and repetitive one at that. It makes absolute sense for AF to carry over your characters.
I personally wouldn't mind if Arcane Force was account wide, but just Arcane Force, not symbols; the other bonuses, like stats and even the damage bonus from having high arcane force are too powerful to be a one and done a day, they'd have to be tied to something like actually having the symbols themselves. I have like 30, almost 40 characters over 200, and at least 10 5th jobbers. I don't think it's fair to get thousands of stats and a damage bonus on all those characters on what amounts to just 30 minutes a day for me.
This would be more like the new blockbuster change, not what OP is asking for.
You can't stabilize catalyzed Arcane Symbols if you already have that particular symbol, so you couldn't use multiple unstable symbols to power level a single symbol.
But for the record, I'm against this proposal. If you want to work on symbols for a different character, either suck it up and do them both, or choose one and work on that one for a while, you don't need to do dailies on all your characters.
Personally, I opted for the latter, and it was fine.
It's fine the way it is. I would wager most people prefer to swap their quests, to get all kill quests, or all drop quests, or minimizing travel, rather than taking them as is, and swapping the buttons means the least wanted option is put in the somewhat "default" spot. The button that occupies that spot should be the one most would want (accept, exchange).