I would argue that Woolies and Cricket Australia have actually suffered some significant reputational damage as a result of their anti Australia Day policies. I think a lot of people don't like seeing corporations and sporting bodies taking political positions.
Totally agree with you about the culture war distraction though. To me this whole drama is not even about the date, it's about the nation. We could move the date but many activists will still be against the nation itself they'll just move on to the next battleground.
RE: Cancelling Australias National Day