That's the crazy/non-intuitive aspect of NN training. Even in the standard-chess training mode, 99.999999999999% of all positions that Leela will encounter in any given game will be positions she's never seen before. It's not a question of "what specific positions will Leela see in training", it's a question of "what variety of positions will she learn to understand?"
Training across all 960 positions will ensure that NOTHING particular about any of the specific starting positions will be learned. However, with 960 positions in play, improvement/expertise could only come about with deep understanding of positional play (and how to work for solid positions regardless of original configuration). There's no chance of traps/tricks that work by happenstance in the standard opening might confuse leela's understanding of fundamental principles.
That said, I wasn't really intending for this to be a full rehash of the question of whether or not c960 would be better for training. This was more an appeal to, "Why not give it a shot?" (assuming "give it a shot" is a attainable goal). In current chess mode, the testserver training always shoots up rapidly then starts to level off after 1 million moves or so... what if, thanks to the increased richness of openings, C960 shot up and continued climbing for 1.5 million games (maintaining a perpetual lead over the standard alternative).