Hmm... I don't understand, do you think the Illusionist's "ability" is better than the Archmage's?
Posts from What mixed hero class of the Haven faction do you like?
Which hero do you like?
Yes, it's better to summon more clones; that's what I remember his "ability" being.

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1. Battle Mage - the easiest class to obtain, the main benefit is protection of the mage from physical damage (do not take additional skills), because the damage from Order's offensive magic is weak, and 20% is useless.
2. Illusionist - can be taken if you are not playing with a Tactician, the main benefit is increasing the army's speed (do not take additional skills), because the Illusionist's power is significantly less than that of a squad of Djinns.
3. Soothsayer - can be developed in the city academy, especially since you cannot hire a Thief.
4. Monk - can be developed in the city academy, good protection against Chaos troops and magic, plus useful spells in the city guild.
5. Sorcerer - the bonus is excellent, but for Chaos. For Order, Chaos magic is less useful, and there are no spells in the guild.
6. Shadow Mage - in general, it is better to hide behind your army from arrows, and Mirage will be more useful than various curses.
7. Enchanter - the same bonus as the Illusionist, but there is no bonus from the Tactician and no spells in the guild.
8. Warlock - well, if a weak mage goes into melee, then... it's better to hire a Barbarian.
9. Archmage of the twelfth level - this is something significant, but you still have to survive until then... It is much better to have 3 simple mages - instead of +20% to the spell, they will give +200%.
In conclusion, I will say that the first 4 (5) advanced classes can be taken depending on the situation, the rest are not of interest.
Справочник по НоММ-4 http://handbookhmm.ru/pamyatka-dlya-heroes-iv.html
Памятка по НоММ-3 http://handbookhmm.ru/pamyatka-dlya-homm-iii.html
и HotA http://handbookhmm.ru/vyishla-obnovlennaya-pamyatka-dlya-homm-iii-hota.html
7. Enchanter - the same bonus as the Illusionist, but there is no bonus from Tactics, and there are no spells in the guild.
8. Warlock - well, if a weak mage goes into melee combat, then... it's better to hire a Barbarian.
8. Warlock - reduces the enemy's luck during melee attacks, and you can give him a bow with some kind of arrow anyway.
Справочник по НоММ-4 http://handbookhmm.ru/pamyatka-dlya-heroes-iv.html
Памятка по НоММ-3 http://handbookhmm.ru/pamyatka-dlya-homm-iii.html
и HotA http://handbookhmm.ru/vyishla-obnovlennaya-pamyatka-dlya-homm-iii-hota.html
8. Warlock - reduces the enemy's luck during melee attacks, and you can give him a bow with some kind of arrow anyway.
Справочник по НоММ-4 http://handbookhmm.ru/pamyatka-dlya-heroes-iv.html
Памятка по НоММ-3 http://handbookhmm.ru/pamyatka-dlya-homm-iii.html
и HotA http://handbookhmm.ru/vyishla-obnovlennaya-pamyatka-dlya-homm-iii-hota.html
Regarding reducing luck in ranged attacks, I haven't tried it (nor did I re-check) - I've never specifically leveled up this class, as it's better to have more useful heroes in the army instead.
and at max level, you still end up with either an archmage or a warmaster.
The Battle Mage is the most useless...
and at maximum level, you still end up with either an Archmage or a Warlord.
The Archmage is, of course, the "ideal" for any mage in campaigns and on epic maps, but in the case of the Order mage, it will primarily enhance the additional schools (which requires developing these schools at a high level). If they are taken "opportunistically," then even the adjacent "Monk" and "Shadow Mage" will be better in certain situations, as they provide simple but permanent spells "built into the hero." And the combination itself, besides being "supported by magic," is quite meaningful, since both Order magics complement each other very well.
Regarding combinations with opposing schools:
The Enchanter is a class for a druid raised in the Knight's Seminary (or a mage retrained as a druid there). To have both sand, slow, and good summons, and to learn everything in the Guild.
The Sorcerer is a pleasant and useful bonus, but Chaos is taken exclusively for the "checkbox," which puts an end to the possibility of developing War skills (it will override "Battle Mage," and you will be left with neither here nor there with Chaos magic). Starting in the Fortress of Death with access to one of the two schools, or capturing another's fortress with the same access, makes this career more meaningful. But the bonus is excellent and worth considering.
The Illusionist, Seer, and Warlock have useful bonuses and are chosen based on your needs (the last two, as mentioned before, are usually easily acquired through the University, as are the Monk and Shadow Mage), if you don't want to spread your forces to an adjacent magic.
Yes, it's better to summon more clones; that's what his "ability" is for, as far as I remember.
If a player chooses to focus on creating clones, then the Illusionist is definitely a better tactical choice than the Archmage.
Specifically, is it due to the Tactics skill?
That's right, it's them! The skill enhances their abilities. If you don't get too involved with other schools, the Illusionist will naturally get the necessary boost. And tactics will make the Clones not only more numerous but also better.
In that case, we're talking about an advanced class for the Tactician (buy a Tactician of Life or Death and give him magic from Haven, for example, three altars, learn Illusion, and then develop the Tactician).
But yes, it's certainly more convenient to start with a Tactician right away (besides the altars, the Seminary and University can also help).
But Illusion in Haven magic is far from the most important thing. If you look at advanced classes in terms of bonuses, then either Monk or Shadow Mage are the most useful.