The show could still exist, and in arguably stronger form if it continued to focus on a small-scale planetary conflict or several conflicts simultaneously. All that the crawl in ANH states is that this military force has had no victories against the Empire, implying that the Alliance has been newly organized from many smaller cells just before ANH or that the Alliance has failed to take unified action before the events precipitating ANH. Heck, since the crawl doesn’t specify the Alliance it could simply be that the Organa family has their own isolated cell which has been building in strength for a long time but has only been deployed to specifically combat the Death Star threat. The Organas could have been pacifists until that point while other cells tried and failed to act on their own.
This continued insistence on battles similar to those in the OT continues to kneecap these golden opportunities to craft stories distinct from the now slate grey storytelling of most EU content.