DNS stops resolving because the domain is pending deletion. At that point it's not a renewal, it's a restore (which costs a lot more money). Refer to the brown "Domain no longer in zone" section of ICANN's lifecycle chart: http://archive.icann.org/en/registrars/gtld-lifecycle.jpg If people are actually regularly using restores instead of renews then they're unnecessarily throwing away lots of money.
> I've seen govt agencies use this as their reminder to renew.
What TLDs were these government agencies using? gTLDs have uniform policies but ccTLDs and special purpose TLDs like .gov do not (and you cannot generalize your experience there to gTLDs). But the expired nameserver domain registration under discussion in this article is a .com, which is a gTLD, so it goes through the standard lifecycle of 30 day redemption grace period + 5 day pending delete period, and during these its DNS is yanked.
Source: I've been in the domains industry for 7 years and run 44 TLDs.