War machines in Heroes V.

I often played with the upgraded catapult and learned to destroy both towers and the gate in the first and second turns... Even though I don't like summoning magic, this is more relevant to me. Although, for Necropolis, the direct path is summoning, but I rarely play with them. And I didn't say that in the first case, the mage will die, and in the second, he won't... it's just that the catapult is always available, and what you wrote: earthquake, hypnosis, etc., are already random factors (this is not the point, but I had a case in Heroes 3 where a fully built guild of mages with a library in Tower didn't give me a single offensive spell... since then, I've been wary of randomness 8)). A lot depends on the players here, but for me, during a long game, it was always difficult to storm the mages, because three archers and two flyers, supported by tough melee units and, of course, a pumped-up mage, make you sweat.

So, do you consistently destroy 2 towers and the gate in 2 turns, or are you just lucky? I used to destroy towers and gates, I didn't even know about the earthquake spell, but I got frustrated when I aimed at a tower, and the catapult shot at the opposite wall twice (damn gunner), and sometimes it would destroy the tower in one shot, but instead of targeting another tower or the gate, it would keep shooting at the same spot, or it wouldn't do enough damage and would hit the wall as if I was going to go through it, even though there's a moat there... so, after realizing and learning about the earthquake spell, I thought and decided to save my remaining nerves and not upgrade the catapult specifically, only if it's already built.
Regarding capturing castles in Heroes 5, with any race, a pumped-up hero, and a decent army, it's difficult to conquer and defend all of them, so I don't focus on castles; I defend my own, and the rest depend on the situation. In Heroes 4, it was generally easier to defeat an army in a castle than on the plains.

Added 1 minute ago
Yes, now I will capture the mage castle with particular interest.