Earlier quoted context omitted.
You're not making the same investment at the outset: you're doubling down after the business has already demonstrated "I'm failing quickly, unlike the median funded startup, which is failing marginally less quickly." [+] In return for assuming that extra risk, you get no marginal gain in equity. If you absolutely must shoot your own foot, clean the wound after doing so, because gangrene sucks even more than gunshots…
I still don't get why it's a bad idea to forgo salary in a venture where you retain majority ownership. It sure seems like there are loads and loads of people who spun up successful businesses on sweat equity. Way more than have ever taken funding. If it's not a capital intensive business and your cost of living is low, why on earth wouldn't you minimize investors to the extent possible? If you've got $300k in saving…
At a funded startup, though, you've already committed to "We either grow big or fail ingloriously." If your personal paycheck is the difference between solvency and insolvency, you've already failed ingloriously. That's fine and expected, but don't put your family's financial situation at further risk by deferring the paycheck for the final few months.