I've seen my 5s charge a lot quicker using the iPad charger. If there's a real source for the 'can't take the charge any faster' claim, I'd like to see it.
I honestly don't think you have.
Take at look at this post, where the iPhone is refusing anything over 5W from a MacBook Pro.
Of course the device dictates how quick it charges. It's the same voltage just capable of more possible current. I'm an Electrical Engineer, I know how a fricking battery charger works.
I'm not sure what you're saying there, but if it can/will only accept a 5W charge, it doesn't matter whether you've got a 5, 10, 12, or 1 million (exaggerated to prove a point) watt charger on the end, it will on,y ask for 5W.