Side note here, of all the mistakes made in that battle (like not setting the shields frequency to rotate randomly or unleashing a full weapons barrage at the BoP) not targeting the bridge immediately was the biggest mistake.
I disagree, but for out of universe reasons, not in-universe ones. Star Trek, IMO, should NEVER EVER depict anyone targeting or directly doing damage to another ship's bridge, because doing so just puts a big, bright spotlight on what is an idiotic design choice. Roddenberry's "arbitrary rules," as
Gary put it; this is one that makes no sense. There is no practical advantage to having the bridge on top, there are only disadvantages. However!
That said, it's one of those "Trek traditions" that - despite its silliness - I don't feel the need to change. Like the entire concept of the Universal Translator, I think that having the bridge up there (and it's not just Starfleet; it seems to be on top or up in front or similarly exposed on other ships, as well... hell, Star Wars and Babylon 5 do this too, but that's another discussion.

) should just be one of those things that we
all know is silly, but we just wink and elbow each other and ignore it, because it looks good after so many years of Trek. Having the bridge be targeted/hit (either
just the line, as in GEN, or actually showing the bridge get slagged, as in NEM) is a horrible idea, production/writing wise, because it shines that light onto a problem that can be otherwise ignored.
^ It's not the job of a ship's hull to protect the bridge. That's what shields are for.
Any attack powerful enough to punch through a ship's shields will be able to hit the bridge no matter where it is.
That implies that any and every hit that gets through the shields and does some damage WILL penetrate deep into the ship (i.e. deck ten on a twenty-deck ship). This is clearly not the case. Weapons powerful enough to be a threat to the ship and do damage to it's shields do impart SOME damage to the hull on impact with said shields. Shields do not have to fail completely for some damage to bleed through, especially as the battle wears on. This bleed through damage could, at times, be enough to punch a hole through the inner hull; if the bridge is on the tippy-top as it is in Trek, then you could open a hole to space in it. If the bridge is deep inside the ship, this cannot happen.
But, as my initial paragraph suggests, I'd rather just leave the "bridge on top" issue alone entirely. Don't mention it, don't call attention to it.