Personally, I do a mixture of both -- some icons, especially on the top rows, are easier to reach with the mouse than on the keyboard, so I click them. But most of the lower icons are easier to just reach up and click the number buttons on the keyboard, so that's what I do with those. Still Paul isn't really interested in the ways people do it -- he's interested in what's best. In Arena, getting abilities cast and out as fast as possible is often more important than anything else, so it definitely seems like relying on the mouse for movement (and maybe even binding oft-used abilities to mouse keys) would be much faster than clicking on icons periodically. Of course, there's always the option to do both at the same time.
It would be interesting for sure to see what kind of schemes and setups winning Arena teams use -- I'd imagine that they'd have to play with default interfaces, so while keybindings and macros would probably work best, they wouldn't be able to go too overboard with customization. At the highest levels, is it faster to click and press or just use the mouse for movement?