The Warden didn't have reason to believe he could even get Eamon's support, assuming even that Eamon was alive (remember, there were treaties for the other factions, but not Eamon). Saving the town wasn't directly relevant to stopping the Blight, and put the Warden in significant danger.
IIRC (it's been awhile), it was Alistair who mentioned Eamon and by then the Warden knew of their special relationship. The Warden might believe that Alistair would have some influence with Eamon.
Moreover, if Eamon's a competent ruler, he should see the value in stopping the Archdemon even if Redcliffe has already been destroyed. And if he's not a competent ruler, why do we want his help?
The Warden needed Eamon's support, not only militarily, but also politically. Loghain, Howe, etc., were making things pretty difficult for the Warden.
Also note that local militias figured into the armies that marched to Denerim. Helping the Redcliffe militia gave you more troops in the end.
Finally, it seems to me like Bann Teagan should be able to help the Warden even if Eamon doesn't wake up. Helping the Redcliffe militia defend the town should help cement his support.
I would suggest that taking out the enemy fleet while it is isolated from the biggest capital ship every encountered and you have surprise, speed advantage and allies still on the field is always going to be tactically more sound than ignoring the enemy fleet and hoping it doesn't jump you after it's finished off your friends and you've moved into a confined space and turned your engines off.
Indeed. Ignoring the other enemies firing on you while you're trying to make your way to the primary target is a recipe for disaster. They needed to thin out the geth fleet anyway, and may as well preserve the flagship in the process.
I feel like Hackett can make a comment about the Destiny Ascension having helped defeat Sovereign at the end of the Arrival DLC - but don't remember exactly.