"...distillation is one of the best desalination techniques there is."
I don't for one moment doubt the validity of this statement. However, you will note that no claim is made as to the absolute
removal of salt via distillation as is typically practiced in a malt whisky distillery, simply because multiple sequences of distillation and redistillation (and even then, better through a purpose-built purification still more along the lines of a column rather than a pot still or alembic) represent the only way to ensure 100% separation and removal of suspended impurities (including minerals). And surely, this is not what any malt distillery 'worth its salt' (sorry, I couldn't resist) is all about.
There are many compounds that percolate through the whisky distilling process. And these are precisely what help to imbue each single malt with many of its unique characteristics. Hard water or soft. Brackish, peat-laden water or clear. Factor in the manner in which these different waters interact with the stills employed at various sites, and you have a sure-fire recipe for variety - even before the distillates from these places meet wood.
I can taste saltiness in many whiskies, and that's a good thing!