Sorry, but the tray-icon is an indicator to tell that avast is working – specially if the entire PC is irresponsive and you have to wait for minutes until you can enter the next character when writing something or else!
The user wants to know if something is eating up CPU-charge – and the whirling tray-icon is a very elegant way to show that!
Btw.: Avast 4.8 could additionally show directly which files were being checked; I miss that feature since v5 (but it should be half-transparent and not disturb click-zone (i.e. it should only display, and you always would click-through)!