So, if you encounter such a mixed army, the tactic of weakening it with a magic hero specializing in offensive spells won't work.

What did you expect? To attack a hundred griffons with a not-so-strong army, cast a magic spell on them, and honestly run away, taking a stack of upgraded units with you? And there might be up to 50% of the original number of neutral monsters... This is not a problem with organizing tournaments; it's a problem with the game itself. And it is specifically mentioned for those who like to find loopholes caused by bugs in the game. Now, we will consider this a prohibited tactic.

I just wanted to clarify: if the hero doesn't run away but honestly dies in battle, but can't defeat the upgraded stack, will this stack still disappear?

Yes. As bitter as it is to realize. :)
All the remaining upgraded units will disappear after such an attack.

PS. At least I didn't see this prohibition on previous official tournaments. Does that mean it wasn't prohibited there?

Let's solve problems as they arise. In a blitz tournament, you won't have the opportunity to use these bugs.
And in other tournaments, discuss this with the organizers. It's all up to their discretion. I'm not going to prove anything; I'm just sharing information with you. Think for yourselves.