HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

I would like to increase the number of hired heroes from the maximum of 8 to 16.

In fact, you can already hire more than 8 heroes in the game, but all of them, starting with the 9th, are forced to literally sit in the cities and not venture out.
And you will stop complaining, ;) as soon as you understand that with a larger number of heroes, the opponent will also play more effectively and will be able to defeat you sooner!;)
And yes: there are players who play with only one or two heroes - and that's enough for them! :D The main thing is not the number of heroes, but the skill!

I notice some oddities when taking a restart and creating a new game, that the new distribution is similar to the previous one... I even tried to completely close the heroes and then create a new one... now, after creating a new game, the previous generation was repeated...
I think something is wrong with the mod, or maybe it was always like this, but I didn't notice.

Perhaps there is an unintentional error in the mod that causes the initial random number to be repeated. And have you tried playing on an older version of the mod - will the generations be different?