I have re-started this game like many many times, finished it only few times (6)
And still planning to play it over (even as I won't have the thrill from exploring, and I will know all the quest solutions ahead, - the most important : artefacts, spells and army income is randomized so the gameplay average has the ability to not get below specific limit, no matter how many times you will replay it.
But here are the main reasons for replaying the game from the start:
there are 3 main characters (mage, paladin, warrior) each with specific skills, style, strategy
There are four difficulties (easy ~ Impossible)
Till you haven't played for each of the main characters - you will miss a lot of the game
For the difficulties it is optional (not everyone is eager to re-think each step of combat or adventure move like in chess game with Gasparov - 300 turns ahead)
But at least
easy (enjoying the instant winning without great effort for epxerienced players - or removing the fear from unknown game for startes) and
Normal (Ok, I have finished easy, let see if I can do it on normal - as well... it is normal -> everyone should be able to finish it on normal... )
But for me the reason why I re-started the game after all was not the character or difficulty reason, not even the "let's find all artefacts and wifes and children" reason, but the fact that I can focus on specific army : UNDEAD, DEMON (not just changing the armies as I play - but try to get specific army asap in the game and hold it till the end... it is making the game much more interesting as you will lose the combination bonuses, but gain morale and better artefact bonuses - or at least - you will see if it is possible (as the number of creatures are limited) - but this is me - as I have very strong HOMM axiom running in my blood - hence I tend to keep one-type creatures in my army