You can still be pretty good and declining at the same time. People are used to elite A-Rod so they think the A-Rod they see now is awful, which he isn't. He's useful. All this injury does is create another problem for the Yankees. It's bad news for them.
Correct, and anyone who doubts this should look at how badly the Yankees offense struggled without A-Rod last season. Just because he's declining and is signed to the worst contract in baseball doesn't mean that the Yankees don't need him.
The only possible silver lining to this news is that it might convince a better infielder (like Scutaro or Drew) to sign with New York, knowing that they will get a ton of at bats with A-Rod and Jeter hurt to start the year/spending a lot of time at DH once they're back.