'In the games of madness' discussions and FG in general

[Radiance]

And again, I ask the question. If the oil or batteries are freely given to the player, and if the game is perfectly playable without them, then why are they even in the game?

More interactivity.
I agree, oil and battery mechanics is not very well done if it doesn't change the game aspect or it's not connected to the lore.

For example, in Dark souls the Catacombs area, if you don't gain particular item you will have a difficult time.

Spoiler below!

http://darksouls.wikia.com/wiki/Skull_Lantern

But, the item is gained in particular way and you can miss it. It changes the game mechanics substantually.

FG addressed this exact thing in their Amnesia post-mortem. They said that the sanity mechanic was a mistake. When the player ran out of oil/tinderboxes or chose to forgo them entirely, the resulting insanity mechanic didn't add anything to the game. It was just an annoyance that the player had to deal with until they found more of the arbitrary collectible game items. All the reasons I've said about why the battery mechanic is a bad one are the same reasons why FG themselves decided to drop the sanity mechanic from SOMA entirely.

Sanity is nice touch but time of the screen effect is too long to watch. It could be used in different way in story element. If went insane, char could remember something or see the world in different way.
Player could experience different aspect of the game.

In Amnesia, screen time when enemy spots you, is to long to watch every time but it serves the lore.

Being able to outmaneuver the AI is a sign of good level design. It means that you can lure the AI away from where you need to go, giving you a window of safety in which to explore and figure out what to do next. Being able to cheese the AI is a sign of bad AI design, since it gives you a 100% efficient way to negate the AI entirely. That breaks the immersion, since the atmosphere of horror and dread is completely undermined by the knowledge that the AI is never a real threat.

I meant 'cheese' as 'outmaneuver'. Player would need to learn and discover the strategy of A.I. to succesfully find out the way how to get rid of it. And every game element tied to that should be eleborate and interesting to the player.
And possibly connected to the game lore, rules and level design.

Exploration extremely important for immersion, I agree. But personally, I feel like encouraging exploration in area where monsters are constant threat is bad game design.

Not if the A.I. encounter is thrilling and challanging.
To extent, I would prefer hard challange but rewarding one. This is not the core horror, I know, but it keeps the player motivated along with story elements.
For example, Dark souls was horror experience for me when I first tried it.
I literally didn't have so much dread moments as I had in DS in first playthrough.
But it balances the challange and reward along with this horror feel.
Altough, Amnesia and SOMA are oriented with building the horror feeling, DS is based on surprise and jumpscares.

I had this experience in Tau, where I really wanted to explore the area and get more lore information, but I had to constantly run around back to hiding locations because the monster would not get off my back. It detracted from the entire experience, because it went from "holy crap the monster is going to eat my face" to "will this monster just give me five seconds to explore this goddamn room". In that case, the ability to explore actually broke my immersion and made that whole sequence a massive chore.

This was the point were it would be good for the player to discover a challenging way how to get rid of the A.I.
Whether that be slowing down the A.I., electrify it, trap it, stun it... using some particular hidden item or learn a way how to build one.

Puzzles, yes. Hacks, no. Like I said before with cheesing the AI, the ability to break the game and achieve an unintended result breaks immersion. Amnesia-style horror games aren't technical games that are designed with speed-runners in mind. They're designed for an engrossing atmospheric experience. Without that, it's just a walking simulator.

I though the hack is, for example, electrify the puddle of water with A.I. standing in it?

Also, and this is another point in which I think that we will fundamentally disagree, but I don't see the point in introducing replayability in a horror game, particularly one with only a single ending. The entire point of the game is to keep the player on the edge of their seats with the unknown, and that is not something that is possible if the player already knows what's coming. In a horror game like FNaF, sure, the nature of the game itself introduces the required unknown so that replayability is entirely possible, but in a story-driven horror game like Amnesia or SOMA, that's just not the case. There can be story choices that lead to never-before-seen areas, sure, but minor choices like whether to escape a monster using option A or option B? That's an in-the-moment decision, not a puzzle that necessitates a second playthrough.

New game+ doesn't change the story but it could thighten the game rules with harder challanges. Players often like this and can have competitive achievements.

Basically, NG+ serves as an answer to the following question>
How to make another playthrough more interesting and variable for the players who had finished the game and know the story?