I do enjoy turning off the map in games.

Assassins creed is playable without the mini map as the targets and missions spot icons are on screen, and it makes stealth and planning your approach into a building really fun. Eagle vision becomes way more useful, and I would recommend anyone bored of the games turn off the minimap, first time I did it was in Unity and I played it nonstop for a week.

Like in Majora's Mask.

For me, finding and unlocking towers was the best part off the game

Unfortunately you can't customize the hud in Botw, it's all on or all off. The time and upcoming weather are pretty useful to have as well as the direction the markers you placed are in.

I've just been playing in Akela for 4 hours, puposefully passed by the tower and went my way with a blank map. I found it a lot more satisfying learning the lay of the land that way and had no trouble following the directions for the shrine and side quests. The maze was also a lot more fun without the big spoiler map. I'm still going to unlock the tower ofcourse since it's fun to climb and to check if I've missed anything important.

Buying or finding maps is better than towers, in my opinion. I liked how older games often handled it as well; you had a classic style world map without zoom and then an automap for smaller areas but you still needed to explore and search thoroughly for treasure and points of interest. Once again, my all time favorite game did this really well and ahead of its time; Betrayal at Krondor used this system and had a spell (and a looking glass) that revealed nearby points on the smaller map (Eyes of Ishap). It also had chests scattered across the world with word locks that needed riddles to be solved to open, some of the riddles were really, really hard.
This whole tower map thing has become so widespread and I find it a really cheap mechanic for all developers to use for lack of better ideas and systems.
Horizon has the same BS system, the only difference being that tower is moving...

Auto-mapping of the detailed map, with just cities, large villages and the most important and known places marked in the low-detail map before exploring is the best for me.

The game does have that... Go to the inventory and then press L to access the mission menu... You can select which mission to focus on... 

Depends on which kind of game it is. In Pokémon, I like that you get the whole map (with routes and cities) from the beginning, but I wouldn't like that in a more exploration based game like BotW.

I mean new sidequests that you haven't found yet.

A combination of Automap and map towers would be fine. Basically, Automap is the standard way to uncover the land, but when you are on top of a tower a huge, circular portion of the map around the tower will be uncovered due to the long distance the character(s) can see

Also, option 4: No automapping at all, make your own maps like in RPGs of old (and Etrian Odyssey, which includes this into it's gameplay) or find maps of the aeras to find out where you are