I'd actually go in the other direction because Acid Stream/Toxic Wave specify that the acid dissipates, whereas Elemental Strike (and Corrosive Spit, for you evil GMs out there) does not.
Elemental Strike is generic, wanting you to fill in your own element. It would be out of place for it to specify restrictions on Acid, without also outright stating how each element functions with the power. Of course, there wasn't enough room for it to do that.
The damage over time for Acid damage assumes lingering acid clinging to the surface. Logistically, I don't see Elemental Strike/Weapon/Body replicating that, since you would basically be dripping magic acid just by standing there, which would not be good for your surroundings. Turn on elemental body, accidentally eat a hole through the floor. Seems kind of odd to me.
Of course, none of this is specified in the rules and its a total GM call how it should actually work. I'm leaning towards 'Acid Evaporates' both for logistic reasons and balance reasons. Unlike fire, acid automatically starts dealing its damage over time, rather than having to beat the target's armor to ignite it, which would make Acid massively more useful to the player for dealing damage.
A Strength 6 adept wielding a Katana using Acid Weapon would deal 9P of base acid damage and reduce the target's armor by 1. Next turn, he rolls against 8P acid, now with 2 fewer armor. Turn after that, 7P, with 3 less armor. The adept could hit most targets once, then just stand back and wait for his opponent to melt.