"This is quite a recent affectation: Robert Burns and Sir Walter Scott, eg, often referred to Scottish people as "Scotch"! "

Which in itself was an affectation though! Scotch was a contraction of 'Scottish' introduced from England along with other anglicisation which was going on. The native terms (I know there was gaelic terms too) was Scottish or Scottis/Scots. You are right though Scotch spread in to common usage within Scotland itself. It has now long been viewed as old fashioned and the terms Scots/Scottish are generally preferred by at least most people - with Scotch being used solely as an adjective to describe things other than people. So scotch eggs; scotch pies; scotch mist and of course scotch whisky - but people are Scottish or Scots. I think this change in usage happened within the last century and certainly after the main diaspora so north Americans of Scottish heritage still use Scotch much more than most Scots themselves would.