Do all the games in this series have in common that you can only move your knight a limited length per turn, and even the dumbest al are able to make you a visit even before the coffee beans are roasted?
And is it impossible to be the only player on a comfy map with just the monsters and places to explore in peace?
If so, I may not even bother install the rest of the series.

It's a strategy game, not RPG, and you compete with other heroes to be the king of the hill. It would be no point in just wandering around with no enemy.

This is true upto a point. The campaigns are usually a lot slower than single scenario's so you shouldn't be overwhelmed before you get going. And especially in H3 you will not usually run into enemy hero within the first week, or 7 turns, of a game unless your playing on a very small map.

I do remember that in H2 there was a map that started you with 5 Heroes but the other 3 AI's also had 5 Heroes within walking distance of your starting town.

To your original question yes the Heroes have a set movement allowance per turn, however this can be increased in Heroes 2 and beyond with Logistics and Pathfinding skills. In H3 and H4 leaving your slower troops behind also speeds up your Heroes movement points for the turn.

Have you played many other TBS games at all? I ask so that if we have played the same ones I may be able to point out better comparisons or things you may want to look forward to.

Some of my top TBS games are

Master of Orion 2
Master of Magic
Heroes 3 & 4
Eador Genesis
Civilization 2 (sadly cannot find my disk of this anymore and it's not on gog :( )

If you're looking for a more relaxing single player experience where you can explore at your pace, I seem to recall that King's Bounty is very much like that. Then again I only played the old one that used to be the precursor to Heroes of Might and Magic, I did not play the new one, but I saw a friend play and I don't recall there being enemy heroes wandering around.

But yeah, Heroes of Might and Magic isn't King's Bounty. Old King's Bounty was a single player fare where you wandered the land in search of an artifact, hiring and killing monsters on the way, and racing against the clock to achieve a better score. Heroes of Might and Magic is very similar gameplay wise, with one important difference: you're not alone anymore, there's other players out there wandering the land and plotting your demise.

New King's Bounty also totally fills that description, so if he wants a game with that sort of tactical combat without the AI opponents (to be fair, the AI in Heroes I is quite aggressive compared to the easy AI in later games) or overarching strategic stuff they aren't a bad place to look.

Still, I'd at least give Heroes II or III a shot before writing the series off.

I was thinking exactly the same. Don't like HoMM because other heroes run around and steal your stuff? King's Bounty is the perfect game for you.

I must say while I like HoMM, I also get severely annoyed by its campaigns. Often you get into a stalemate with the enemy keep stealing a castle from you while you steal one from him and then a single level can drag on for hours or even tenths of hours. ZzZzZz

It's more aggressive because it's simpler; if you leave a castle undefended enemy heroes will make a beeline for it from the other side of the map. If you beat the enemies main hero, and still leave your castle undefended the enemy will just recruit new heroes and head for your castle, and never clean out its own backyard,
The AI improved in the two next games.

It is possible in HoMM III; not in RoE - I can't remember now which one, but either AB or SoD introduces new victory conditions which allow you to play (custom) scenarios with just one player.