[2019] We have Cospri's Malice for Cold and Mjölner for Lightning. If you could design a similarly themed weapon for Fire, what would it look like?

what would it look like?

Ngamahu's Flame.

No, really. Probably not exactlly like it, but a lot like it.

So far as I'm aware, this wasn't intentionally created to match with the other two you mentioned, but it ticks a lot of boxes that I think fit.

Fire is the element associated with strength, so it would make sense for the fire one to trigger attacks rather than spells, as a point of difference - it's always more interesting to have a cycle where one sticks out a bit than where everything is clean mirrors of each other (see added fire damage support or hatred as exceptions to their cycles, for example).

But because attacks are very animation-driven and triggered skills can't play animations on the character, we can't just trigger arbitrary socketed attacks - they just won't work (and/or will horribly crash). So it supplies it's own attack that's very generic - scaling on attack, physical, fire, projectile, or aoe modifiers - so that it fits into lots of builds. Two-hander reinforces the attacking theme as a point of difference with the other two, and also allows for six sockets to support the built-in skill if desired (with other 6-link in chest for main skill). Also reinforces this being the Fire- (and thus Strength-) aligned version. Being two-haned also means all melee hits are hits with this weapon, so doesn't need to have that part explicitly specified like the other two.

Instead of triggering socketed spells, it "triggers" socketed supports (because they support the built-in triggered attack). Attacks rather than spells, meaning builds are more likely to actually care about more than just attack speed on the triggering hit with the weapon. Similar enough to the others to draw parallels, different enough to feel like it's not just re-treading the same ground.

The hypothetical "specifically created to match the two supporter-designed weapons" version would have some form of higher attribute requirent, and I suspect a 100% chance to trigger, but it's skill would have a longer cooldown than Molten Burst does to compensate (again, this one would want to be less focused on only scaling attack speed, and this would work with that). The triggered attack would probably be a melee skill similar to Vengeance, rather than a projectile like the burst is, so it fits more in a strength-aligned melee build, or otherwise lean into the projectile part and have dex be the second raised attribute requirement, which does fit the cycle.

EDIT: Just to avoid confusion, I should explicitly point out that this is entirely my own rambling answer to the question, not some official GGG position. Others on the team, including those who actually responsible for unique design, might not agree with any or all of what I've written.

That isn't how ancestral call works. The ancestor is entirely a client-side visual effect with no impact on mechanics - the attack is driven by your character's animation.

The problem there is a skill can't have multiple triggers. Since counterattack skills already have a trigger built-in, adding another trigger would disable them.

Conveniently, the only part a triggered bow skill needs is to fire the arrow, which is the simple to fake part of the animation that matches how most skills work. The other stuff in those animations is mostly to do with turning visiblity on and off for the arrow the character has ready in their hand (hide it when you fire, show it again when you reach to the quiver so it looks like you grabbed a new arrow) and making the bowstring animate - both of which a triggered bow skill doesn't really want because they would conflict with any non-triggered bow skill you were doing at the same time.

Melee skills (especially strikes) tend to have more mechanical info in the animation that makes generic triggering of them much harder.

You could, but at that point it's become something very different to triggering the attack - the attack isn't triggered (it's performed by it's user by playing the animation, which is just attacking), and it isn't you doing or triggering it - it's a mirage or similar totem-style object, which has all kinds of mechanical consequences. We could do that, but it would be fundamentally different enough from triggering that we couldn't call it that.