This logic is incorrect because the fan can be set to any strength, therefore, an optimal point can be reached between being overpowered and being weak.
For example, resurrection is equivalent to double lives, so we should base our calculations on this, either making it 50% HP, or 70% damage and HP, or other similar options.

However, such a unit creates an imbalance in terms of damage output, because resurrection is much more effective in reducing losses than double HP. But this problem is similar to that of vampires. Only, unlike vampires, a Tier 7 unit doesn't appear early in the game.

I agree - an equilibrium point can always be found, and regarding damage output, the Undead faction always has the ability to resurrect their army because the hero always has the "Raise Dead" spell from the start (and so does the Archlich). And, of course, vampires are still around. So, everything can be balanced.
I used to think that "Terrifying Presence" was overpowered, but in reality, I think it can also be balanced - let's compare this ability to "Etherealness" - Etherealness means a 50% chance to miss, i.e., a 50% chance to avoid physical damage - let's look at "Terrifying Presence" - a 50% chance to avoid damage, BUT only from those who do not have immunity to mind magic; those who have this immunity will ignore the ability - this applies to the Undead, Constructs, Elementals, and those who have the "Immunity to Mind Magic" ability.
Of course, we also need to consider that the enemy runs away randomly if the ability is triggered, which clearly increases its significance, but it can still be an ability for a city unit. However, in my opinion, "Death Strike" for the Death Knights, which is being discussed in the neighboring topic, should not be given to city units - I believe that it is too overpowered