Why not? Why can't Congress write complete regulatory statutes? Isn't that literally their job? Yes, it is. "Chevron defense" has been a way for Congress to shirk its duty for decades. If the law is ambiguous, courts must resolve the ambiguity. That is exactly what courts are for. To say that it would be better for an opaque, appeal-proof bureaucracy to have the final say was a ludicrous step on the path to our ever-growing executive tumor.
The tone of your quotes from Kagan give the impression that federal agencies are "responsible" and able to use "discretion". But agencies are political animals, subject to the whims of the current president, who can potentially change every four years. Courts are much slower to change, and much less vulnerable to the political whims of the current administration.
So many people are polarized and focused on winning presidential elections so they have their hands on the levers, that they never question whether the levers should be there in the first place. Perhaps politics would not be so polarized if the President did not have so much power, and the stakes were not so high.