The scenario is that (roughly) 90% of the hypergrowth-style startups which raise a first round will fail to achieve enough momentum to successfully raise a second. And due to the business model choices they've committed to, failing to raise at that point is equivalent to going out of business. A first raise is often too small to be able to do everything they'd like, so they suggest decide that it's in their best interest (long term) to forgo a salary where possible, in order to buy a few extra months of progress before you're forced to start shopping for investment again.
Of course, folks give advice based on their own experience, but it doesn't always generalise to folks in different situations, which is potentially why that would seem like silly advice in (what I assume is) your scenario.
(minor edits toward the end for clarification)
So if you don't have the personal finances to deal with that situation, then you make a different decision further upstream, in the past, by choosing to work on an idea which has either easier funding targets (allowing an early salary), or which can generate early profits (allowing an early salary), or which has lower development requirements (allowing you to work on it alongside another paying job).
The decision is about idea selection, where I agree with you. "If you need the money, then pick an idea which allows you to pay yourself quickly." But if you've chosen to play a different game (typical hypergrowth VC stuff), and you want to maximise your odds of winning at that particular game, then it's generally ideal to buy yourself more months business runway instead of more months of personal runway.
Perhaps still not clear, and I know it's an emotionally loaded topic, but hopefully that makes sense.
Wealth is one of the most important factors for someone to found a startup. You aren't going out and starting a company if you have to work 80 plus hours a week to live.
Just look at the clueless opinions of so many tech founders about how "you shouldn't pay yourself a salary at first after you take investment money". Oh really? So we should just buy groceries and pay rent from the trust fund mommy and daddy gave us?