I wonder, how will you prevent me from reaching level 5 magic and black dragons if the map is XL, huh? Even with the Elves, it's impossible! And when Armageddon comes, the entire Barbarian army won't even have time to understand what's happening.

It's very simple. There are no problems with the Elves. Thanks to the very low cost, the Barbarians have enough income of 2000 to buy all the reinforcements (all upgraded creatures).
Let's take, for example, the second-to-last difficulty level (on the last one, the Dungeon won't get enough sulfur and will be out of the game).
Buildings erected in turns.
Week 1
Wolf Riders (if there is a building for them, then immediately Rocs)
Orcs
Rocs
Ogres
Monsters (finding 6 crystals is not a problem)
Stronghold
Hall of Valhalla
Week 2
Buying reinforcements
Market
Castle
Unit upgrades
Week 3
Buying reinforcements (and that's 4 Monsters) and an attack on the Dungeon.
By this point, the Dungeon, with all due respect, will definitely not have a guild of level 5. Either dragons or a guild. Also, don't forget that in a 1-on-1 fight, Barbarian units are stronger than any other units of the same level.

Black dragons move faster, attack two at once (if the enemies are positioned favorably) + plus, they are immune to any magic!

A debatable advantage. Both can be used to your detriment. For example, you can hit a dragon in such a way that it damages its own units. And I wrote about immunity above.

Manticoras are much better than Rocs (more health!)

They are of different levels. That's one. And if a Roc hits with lightning, nothing will remain of the Manticora, that's two. IMHO, the weakest level 6 unit is the Manticora.

and even upgraded Minotaurs hit so hard that it's scary!

But there are more Ogres, they have more health, and they hit harder. Even though they are a lower level. To fight with Minotaurs, you need to take a warrior hero, and then you'll be lacking in magic.

The Barbarian Castle has little magic; at most, you can count on the Ring of Cold and Lightning!

And I'll tell you that these spells are not needed by the Barbarians. They invest everything in attack anyway. They only need Bloodlust and Teleport (to teleport Ogres)

Conclusion. The Dungeon is a long and tedious tech path. The Barbarians are a fast and fun rush strategy.
Everyone chooses what they like.