My handwave is that the TVA didn’t have an accurate understanding of their own mission, just a good-sounding cover story. Their job was to avert variants of Kang, so in actuality, they may not have been maintaining one timeline, as they thought, but we’re actually grading any timeline as acceptable so long as it either led to the version of Kang who ended up as He Who Remains, or no Kang at all. Whatever happened beyond Kang’s eventual fate (or existence) was totally irrelevant to their true mission, so their gee-gaws and doo-dads might not have even shown them timelines where Earth was destroyed or Thanos wasn’t defeated.