Also, Earth should be teeming with competent Admirals to send into the fray. Loss of "the Admiral" should be a temporary setback only: Picard must have ended up exploiting a very brief window of opportunity here.
The problem with that argument is those Admirals are on Earth, not on the battlefront. The data they get will be delayed. Earth has scanners, but they're likely satellite or relayed information from ships on the line. Other than standing orders to targeting weapons systems, they will drastically be at a disadvantage.
We have NORAD and we have the Pentagon, but they don't deal with coordinating battle plans on the front. Afghanistan has it's own central command to deal with that.
What's surprising though was the lack of any defensive satellite or the lack of a starbase over Earth to defend it against attacks.