Wrong. It's the same radio connecting to the same cell towers and using the same data connection. I am limited by the speed of the iPhone's radio hardware and AT&T's reception in whichever area I am.
My computer rendering websites faster than the iPhone does not affect the amount of bandwidth used.
Browsing the internet on my computer does not use "potentially gigabytes of data" ... No matter how you look at it. Only would downloading tons of large files do that.
And even if it did use more data, I have an unlimited data package, so it doesn't matter.