Unless I'm missing something, the point he's making about holding onto keys hasn't much to do with the algorithms you're using.

Correct, it's algorithm-agnostic. FWIW, Salsa20/12 is the officially-sanctioned eSTREAM winner; it's a perfectly fine cipher choice.

If you had to use Salsa20, could you foresee a design where you'd choose Salsa20/12?

Maybe in some high-throughput application, or something under hard performance constraints. IIRC VMWare uses Salsa20/12 for its remote desktop encryption thing.

20 rounds gives a more comfortable security margin, though, so it's a default that lets you sleep well at night. That said, an attack that convincingly broke 12 rounds could be enough to start thinking of switching to something else.