Late-game Town Enhancement.

Was that a joke about the Elf? Dancing with a circular formation tactic rushes in and deals damage.

No, it's not a joke. The Elf will definitely take Tactics, but even if you counter it with your own Tactics, the Dancers will reach them with their aura and boots. And the damage difference can only be significant if the formation allows you to "wedge" into the enemy troops. But allowing that against an Elf is just poor play.

There's nothing interesting in the third attack perk slot for the Info, except for Tactics, which increases the number of attacks; Cave Crawlers, for example, benefit from it.

I agree with this statement: Tactics increases the number of attacks! Both the Elf and the Demon will reach you. But the variability of their attacks will be greater if you don't take Tactics yourself. Is that unpleasant? Yes. Is it critical? Not necessarily. Specifically against the Elf and the Demon, I would regularly take Tactics for the Info – more variety and forcing the enemy to wear blue boots.
But I would occasionally alternate it with Cold. As for some kind of universal build,

Gnomes really don't need Tactics that much.

it seems we've already reached a consensus. Against at least 3 races, Tactics is irrelevant. That's why I'm considering the Cold option; it's always useful. Of course, this doesn't negate the usefulness of Tactics in many builds for the remaining 4 races.

It's not a given that it will work from the first cast, as Rage can absorb a lot of damage. Orcs have enough damaging and not very durable stacks, and they deal a lot of damage while the entire army surrounds the Cyclops.

The essence of Tactics through elements is to hit rarely, but accurately.
Again, a little arithmetic. Let's look at the damage from the Witch's growth (by the way, not the most damaging stack for the Info; Fighters or Lizards will deal more damage) against the Centaurs, who run in to attack, even without Cold:
Witch's growth damage: 23*2*1.8=82.8
We shoot them, of course, at the opposing element, i.e., +200% damage. Total: 248.4
The Centaur stack has 140 HP, and Rage has 400. This is enough for 47 damage absorption. There's no need to calculate; the Centaurs fall with one shot.
This is the point: with this build, the Info is very dependent on luck. If you're lucky with the elements, you can take out damaging stacks. The exception is Cyclops; you'll have to attack them with a crowd. It's profitable to attack damaging stacks when the elements add up. You need to attack Cyclops at the right time, which often doesn't happen immediately, and sometimes it doesn't happen at all because it's too late.
As for the hero's spell, much depends on the Lucky Charm and the presence of Dampening. With Dampening, it's not very effective to attack Centaurs, I agree. You'll probably deal decent damage, but not completely. However, this raises the question: if your opponent has Dampening, why aren't you playing Dark? After all, one of the most important aspects of fighting the Orc is tormenting him with the question, "What are you going to suppress?" But that's a completely different topic. The main thing is that the Info has stacks that, with elements, can take out a damaging, but not very thick, stack of Barbarians in one turn.