You seem to assume "buy everything" to be the neutral strategy. Then everything plays out as you say.
Choosing not to allocate it is kind of irrelevant, just like "play tic-tac-toe instead" is not a chess strategy.
Stock-picking is specifically referring to where you should allocate a given amount if you are investing. There's obviously more to stocks than simply picking them, but as for picking specifically, there's no analog in poker because you don't divide your bet that way. (Aside from raising on a bluff, but that's stretching it).
Whether, when, and how much you should invest is a separate strategy that's related to your confidence and expected return of the picking strategy—but not the same thing.
Just like whether and when you agree to a game of chess vs tic-tac-toe might depend on your confidence in your skills; but that decision is _not_ relevant to chess strategy, which assumes you're already playing the game.
Buy nothing is not even a strategy. It's like calling empty set a neutral real number