not to mention Picard also had a fully intact starship at his command.
Then again, some of the other ships in the fight did not appear all that beaten up. Indeed, most
of them, in the long shots, were rendered without damage to their hulls.
The fight had just moments ago reached the Sol system; it would stand to reason that some ships had only joined the fight at this point, taking over from the bunch that had last been involved in the running battle (which itself was probably conducted in relays, even if the Defiant
was present at both the beginning and the end). Such ships would be even "fresher" than the E-E, as they'd be both undamaged and
unfatigued from a long RNZ-Earth run...
Of course, the E-E did appear to be the biggest and baddest ship remaining, even if there were fresher ones out there. Although that's a matter of interpretation, as there was at least one intact-looking Nebula
there, and those are bigger at least.
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.