Rutherford didn't do much of significance in Pittsburgh after their second cup. I know there's this assumption that a fanbase would be placated after winning cups but I don't see it being all that realistic. He's still judged on his entire body of work, cups or no cups. Cups are great but the world of sports is still about results and what you've done for me lately. It's just how she goes.
If we win a cup and stumble shortly after there will absolutely be some fans who don't care about what happens going forward because they'll have that cup, but more than likely a larger portion of the fanbase will continue to pivot the way it always has. It's part of what makes following sports interesting, there's always the next thing.
Could ask St. Louis fans how they feel about the state of their organization, they didn't win that long ago.