Smallpiper is bang on target: most of us pipers gag at the thought of playing Amazing Grace and Scotland the Brave. It's the listeners who demand or expect it.
Both are great tunes, though, especially if played in a massed band setting with pipe bands and brass and reed bands in counterpoint. They're just overplayed, when there are hundreds of equally evocative tunes that could be selected.
A second reason these two tunes are called for on days like today is that they're among the (short) list of tunes that virtually every piper and pipe band can be expected to know how to play... even if they've never had the opportunity to practise together.