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And when you bring down the variance to "normal" levels, then the random walk model can be used with high precision even in NLH.

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Well, it depends on our assumptions about how the game is set up. If we assume that you are playing against opponents with infinitely large bankrolls, then the random walk model no longer holds. On any hand, there is a very small chance that you will lose your entire stack. Your winnings at any rate of BB/100 will not eliminate that chance, and therefore you will bust out eventually.

If you play against opponents who add or subtract from their stacks so they're at 1 trillion BB at the beginning of each new hand, then you're correct, assuming both you and your opponents play to maximize EV, rather than to maximize or minimize the chance you will bust.