Oh, sure, blame the computer. LIAR!

: When was the last time you saw a Covenant Frigate or Corvette called a
: capital ship?

: If the term is up for interpretation, I'll go with the traditional one of
: capital ships being the primary, most important ships of a navy. We're
: talking about ships of the line, battleships, aircraft carriers, maybe
: some kinds of cruisers.

We are definitely agreed on that point. Capital ships for me, personally, have always implied the capability to deploy in some function as a command vessel; embarking a function commander (such as the air warfare commander aboard U.S. Navy cruisers) or a flag staff to control carrier/surface groups, task forces, or entire fleets.

: Said logistical and personnel incapacities existed because the Shadow of
: Intent was battle-damaged by the Schism, undercrewed, and sent out on a
: long mission without support. Furthermore, the Prelate lured Rtas into
: territory with a unique hazard that he was familiar with.

All of that speaks volumes in my eyes about what these ships are capable of. The 5km-long CAS is seriously undermined when her ship's company is minimally crewed. The fighting ability of a CRS can be amplified considerably by the pairing of a remarkable captain and the exploitation of environmental or situational factors. While the logistical impairments Shadow of Intent faced are an important variable to consider, as is the battle damaged incurred at the Ark, I don't think we can necessarily discredit the likes of a CRS or FFG on those reasons alone.

: If a lone warship is sent out on an aimless mission in the middle of a civil
: war, and the powers that be don't bother to staff her with more than a
: fraction of her intended crew, she is not going to be combat effective.
: And when she runs up against a wily little snake who knows what he's
: doing, you don't blame the resulting disaster on poor ship design. You
: blame the people who sent her out like that in the first place.

I don't see why you couldn't. Sure, the whole reason of a CAS existing is to embark and deploy air and fleet landing forces, but as a multi-role ship there's a lot more to her. We know that CAS is a competent warfighter in her own right alongside her CCS or CPV escorts. That's worth noting that a CAS, regardless of her battle damage, couldn't have dispatched a patrol vessel like a CRS from three planets away. The fact that a CAS needed an extensively vast crew for simple operations is a design flaw in itself. Covenant policies prohibiting the use of shipboard AI doesn't help either when a CAS has three highly intensive missions to undertake.

: And then Halo becomes indistinguishable from Star Wars which becomes
: indistinguishable from Battlestar Galactica which...

I thought the reimagined Battlestar Galactica did a fairly good job of depicting ships defending themselves from fighters, bombers, etc. Galactica and Pegasus both dished out three weapons systems in defense of their ship. Heavy artillery engaged at long ranges, point defense guns dispatched both Raiders and anti-ship missiles at knife-fighting range, and the air group provided CAP and intercept capability.

The Cylons on the other hand relied too much on missiles and Raiders. I believe that's why they had ultimately decided to employ Caprica Six to subvert the colonial defense network instead of having their fleet engage head-on with the colonials. Galactica and Pegasus obliterated 2-3 basestars during the raid on the Ressurrection Ship with minimal losses, both to their ships and to their respective air groups.

Battlestar Galactica seems to be an exception in science fiction depicting carefully-crafted opposing fleets with their own doctrine and capabilities. As with everything else in that series BSG just so happens to be set in space. I'm sure you could easily apply these stories to a Second World War or contemporary setting.

: I'm tired of seeing science fiction media remake the same five minutes of
: footage for space combat over and over and over again. Halo has the
: opportunity to do something unique, and it's almost criminal how the
: opportunity has been squandered.

Unfortunately Halo hasn't truly centered naval engagements in great detail in a visual medium. In the games it only ever exists to provide scope to the greater setting. The differences between Humans, Sangheili, and Forerunners, among others, in this environment can sometimes seem quite unique. We just don't get writers, artists, etc. who understand that. Greg Bear offered an often mindblowing depiction of Forerunner tactics during their war against the Flood. Nylund and Staten provided that with battles during prior to, during, and following the Human-Covenant War.