In Heroes 3, there isn't a mechanic that prevents a hero from appearing in the tavern one week but allows the player to purchase them the following week.
My apologies, but I described exactly this situation above. Some heroes don't appear in the tavern if a bonus of 1000 gold is awarded. Afterward, they can definitely be purchased, although I haven't verified this.
In general, the point isn't about these specific details, but about the principle. Mods allow you to do things that aren't possible in the vanilla game. And this can affect the gameplay. Is this a fact? Yes, it is. I don't see any reason to abandon the original gameplay in order to save a few moments on digging for resources, transferring artifacts, dividing the army, etc.