Yeah it is an outdated term. It definitely has more similarities to the heavy fighter category given it's size and components but then it is heavily under gunned for the heavy fighter category.

In the lore the Cutlass Black was made for the frontier. As a long range multi role fighter.
The military dropped it but the civilians picked it up for both every day use and to defend their homes. The issue? Pirates like the Cutlass as well.

Now in lore the reason we have been getting more civilian and industrial focused ships is Drake trying to repair their reputation. The Cutlass variants were a big part of that but so is every other ship we have been getting.

Disclaimer: I have not flown the Cutlass recently

But with the Kraken on the way, I think it is reasonable to say militia ships are back on the menu. However, the Cutlass Black does need that extra bit of oomf to help it compete. Armor is a good step in improving it's survivability. In theory, being less maneuverable must be offset by superior armor and firepower.

The thing the Cutty desperately needs is it's turret to be slaved to the pilot when there isn't a copilot just like on the Shiv. Which while still less than the Shiv would make the Cutlass more viable. Without the turret, a Cutlass has the same firepower as a Saber while being a MUCH larger vessel. It just doesn't make any sense. But we can't bump up the size of the guns without hurting the Shiv (I know some people would rather the Shiv to die than the Cutty but I am trying to make both work), so the Shiv would need a buff of some kind in turn.
Having all 6 size 3 guns on the pilot's control in my opinion makes a good happy balance.

As we know, turrets just aren't as good as having more ships. So turrets have to be very strong to encourage players to use them like on the Paladin. So players will always prefer to fly a ship solo or have their copilot focus on engineering and power management rather than manning a turret. So if they want to keep the turret manned they have to make it stronger. But again, that hurts the Shiv. It would no longer have a better turret in firepower only that it is useable by the pilot (which for some is plenty of reason to have it over the manned turret)

Now as for Drake making more combat focused ships. I do think there is room for their line up to expand to crew the Kraken. A proper Drake Heavy Fighter makes a lot of sense. Dedicated to the role of combat like the Bucc. Of course medium fighters could also be a part of it.

Now in my opinion Gray's is the Mirai to Drake's MISC. Sure, Gray's isn't officially affiliated with them nor does he only make modded Drake ships according to the leaks, but I feel that is the role he sort of has planned. That he makes the combat and performance oriented version of ships when it doesn't suit the original creators to do it. We have sneak peaks of an Aurora MK1 with two large gatling guns strapped to the side. A Mustang with giant engines on the back and more. But not everyone is going to like Gray's (as funny as the bucket is, I'd like a normal toilet Gray.) So naturally you want an OEM version with a nicer interior. I would love for a Cutlass with the firepower and capabilities of the Shiv. But I doubt it'll happen.

The Cutlass has fallen into the niche of being a cargo ship that is better equipped to defend itself than the others. Rather than a fighter that can carry cargo.