So, if they match and the program supposedly doesn't change morale/luck during battle, then what is the advantage of this program and why do players use it without modifications?

To speed up the gameplay. The battle time becomes significantly shorter.

Were the battles conducted only in the arena, or on other maps (attacking a monster, a hero, etc.)?

When I said "several," I meant exactly 3: in the arena and on a random map against neutral creatures and an enemy hero.

Many things are unclear to me in this file, and I wouldn't be surprised if, in a few months, at the next tournament, it turns out that "cranim" does change the game's structure, and the computer (let's say), when taking its turn, goes in such a direction that the organizer, who doesn't have this "cranim" installed, won't be able to repeat the computer's actions.

The file is responsible for animations, not for AI. I understand your concern, so I'll tell you about a personal example.
I learned about the existence of "cranim" in the 8th stage of the World Cup because I had a difficult task: killing golems using a ballista. Although I knew exactly how to do it, it was incredibly time-consuming because the golems move slowly. Moreover, they are so slow that the corresponding time parameter entered into the program before launch exceeded the limit, and I would have had to do everything manually in the final playthrough, because asking vbn to change the program would be pure cheating, as it would be impossible to guess why I needed it. And the battles with "cranim" took hours, and without it, it's even scary to think about (by the way, I never hid the fact that I use "cranim," because, for example, anyone who read my description and answers about the duration of battles and at least tried to play a couple of rounds could guess it). So, the selection of the computer's moves for all 6 turns (and if you remember, it was very specific, because 3 enemy heroes on the 7th day lined up in a row to be killed in front of the castle) was done even without "cranim," and in the final version, the computer behaved ABSOLUTELY identically (as you could personally see), and even the time to select the necessary moves was comparable.

I, of course, slightly exaggerated that everyone on the Portal uses "cranim" (Catch says he didn't even know about it), but I am sure that many strong offline players and almost all (or maybe all) top online players use it extensively.
After all, real time is very precious, and "cranim" really reduces it.