You are mixing up 18th and early 19th centery terminology with 20th century teminology.
The word battleship is short for line-of-battle-ship, another term for ship-of-the-line. So Hornblower era ships-of-the-line were the equivalents of 20th century battleships. All Hornblower era ships--of-the-line. Including first, second, and third rates.
You called the Enterprise a second rate ship in the Hornblower era analogy, and so you called it a ship-of-the-line, which is the same as a line-of-battle-ship, wihich was the Horblower era equivalent of a battleship. Thus you called the Enterprise a battleship in the Hornblower era analogy.
It is true that in the 20th century analogy the Enterprise is described as the equivalent of a 20th century heavy cruiser which is 2 steps down from a 20th century battleship. It is also true that when the Enterprise was described as a heavy cruiser analog when a heavy cruiser was the most powerful big gun ship in the US navy. The only ships with more power in the US navy were missile submarines and aircraft carriers.
Missile submarines and aircraft carriers have no function in space warfare. There obviously won't be any missile submarine or aircraft carrier analogs in space warfare. So the 1960s US navel vessels that were the top of the line and most powerful in any form of naval warfare which has an possible analogy in hypothetical space warfare were
the cruisers, with the heavy cruisers the very top.
So describing the Enterprise as a 1960s heavy cruiser equivalent is more or less the same as describing it as a 1940s Iowa class or Yamato class battleship equivalent, the most powerful type of its era.
I'm going to back up and define my terms. We have the danger of talking past each other, particularly if one of us starts ascribing intent to the other.
I said "second rate" casually, probably too casually, and I apologize for the ensuing confusion (since rate back then, as you noted, refers to guns mounted and down to third rate is a ship of the line).
I meant "Not a ship of the line" in the Hornblower sense. i.e. filling the same role as a frigate, which is
not a ship of the line. If the Enterprise is analogous to the Lydia, it's not a ship of the line.
The reason I brought in the discussion of 20th Century heavy cruisers was as it seems to be reinforcement of the view of the Enterprise as frigate/not ship-of-the-line/not battleship. Yes, in the 1960s, battleships were largely scrapped and cruisers (missile and AA) were the biggest non-carrier vessels in the USN (though saying there won't be carriers or missile submarines in the Trekiverse is not a statement supported by evidence: what are Romulan Warbirds if not missile/attack submarine analogs, and we don't
know if there are/aren't fighter craft equivalent in Trek -- certainly shuttlecraft are FTL, and Star Fleet Battles (not canon, I know) introduced carriers for all races. And in any event, carriers ruled the roost by the 1960s -- no one in the 60s would be thinking of a cruiser as the queen of the fleet, even if they thought there would be no carrier analogs in the future).
In any event, the
Heavy Cruiser largely doesn't exist in the 1960s. It is a ship that had its heyday in the 1920s-1940s. And in that era, the CA was definitely not a ship of the line equivalent. It was a scout, a commerce raider, a small-vessel hunter -- a third class vessel compared to battleships and battlecruisers (and panzerschiffe, which one could call heavy cruisers, but were dubbed "pocket battleships" for a reason). The Enterprise being a Heavy Cruiser suggests that there are battleships and perhaps other larger vessels in the Federation fleet. Certainly TAS made that assumption, and Franz Josef followed suit.
Anyway, I bring these points up because we don't
know what the Enterprise's role vis. a. vis. the Federation fleet is. Could it be a battleship equivalent? Certainly
The Ultimate Computer suggests that they operate in fleet actions... but so did the three ships that chased down the
Graf Spee.
But if Hornblower be the model, then the Enterprise is a frigate, not a ship of the line. If the class Heavy Cruiser is any indication, then the Enterprise is not a battleship (the modern ship of the line).
That's what I meant by second rate.
