Magnis, I do agree with many of your points, and although I personally don't want a federation battleship, as mentioned previously, the fact remains that the federation is currently in conflict with several enemies . . . What happened in the history of naval vessels? Well, we started out with exploration and trading ships, the same as with land exploration, but what was the first thing most nations did when they found an enemy, or a potential enemy, they created warships, battleships, weapons to defend themselves with. Thinking down this route then, what would humanity's natural instinct be when faced with this many conflicts? Particularly when they are against some pretty powerful forces? I reckon the federation creating a battleship class wouldn't be quite that far fetched as some die hard fans might believe it to be.
However, given that this is the federation, such a vessel would be made, knowing that it had a limited lifetime as a battleship, once the need for it disappeared, they would either retire them, or more likely refit them for exploration, or some other purpose. Just because it hasn't happened before, doesn't mean it can't happen, at the end of the day, the game is writing the canon now, and as far as I remember, I don't think the federation has had this many enemies at once before.
That said, I would prefer a fleet support vessel as I mentioned previously, it fits the image of the federation better, they don't send single vessels in to deal with threats, they send small fleets that can combat most threats to defend an area. Or they send a single vessel that is capable of defending itself against most small threats to explore new areas. It just isn't the right feel for the federation to have a carrier type vessel, or something that is the equivalent of a Borg cube. Sure, in STO single vessels can take on borg cubes alone, it's difficult, but it's possible. But watch First Contact and you'll see that Borg cubes used to be a pretty big threat, that required tactical thinking and a fleet to defeat. And to be perfectly honest, I can't think of any other vessels out there that really fit the battleship description within Star Trek, it just isn't the feel of the series to have vessels like that, shoving a sovereign into contested territory is enough to get most races antsy about whether you're preparing for a conflict, let a lone a full blown battleship.