We didn't replace long established iconography for things like shuffle and repeat settings with textual representations. Why? Because text takes longer for the brain to process!
Presumably, this is only true if the icons are instantly recognizable and/or easily interpretable. If your users have to spend time thinking about what the icon actually means, you're probably better off using a word instead. Unless, of course, you're trying to train them so you can lock them into your particular UI dialect, as mentioned in earlier posts.
Another reason UI designers like to use icons is that icons are generally spoken language-agnostic. You don't have to translate your UI for different locales if you use icons rather than text. Of course, if your icons have tooltips you'll be translating them anyway, but it's always nice to minimize your translation work.
Also, let's not pretend that every interactive UI element can or should be iconified. Take a paint application; you can easily iconify common tools like the Pen or Paint Brush, but the properties of those tools (i.e. threshold, pressure, opacity, etc.) are too far from tangible real-world objects to iconify easily. Attempts to do so will probably end with frustrated users who now have to learn your special icon dialect.
Finally, the oft-quoted statistic that the brain processes images 60,000 times faster than text seems to be somewhat suspect when you start digging into it.