One thing I've observed with a lot of adventure games is that I run into a puzzle that house doesn't click. Then I will end up seeking help. If there is a hint system in the game, I'll use that, and then I'll be on my way. If I find a walkthrough... Well, now I know where it is, add I'll end up using it more than I want.

Which is why I was so happy when the hint system in TWP came online. Particularly since I played with my SO, who is less patient with that kind of frustrating puzzle.

John Walker at Rock, Paper, Shotgun has written a lot about this, e.g. https://www.rockpapershotgun.com/2017/10/02/assassins-creed-origins-tourism-difficulty/.
His two main arguments are in this paragraph:
"I hate them for me because I find them incongruous to the rest of the game they're in (there are exceptions, games where a ‘boss' is in fact a sequence that asks you to employ all you've learned so far, the gaming equivalent of a comprehension test, and these work so well, but they're rare like rubies and it's almost always just a difficulty spike). But I also hate them for other people, those who aren't as good at games as I am (I am average good at games), for whom I know these are not boss fights, but end points. They are massive impassable obstacles between them and the fun they could be having afterward."

I am designing some kind of "real-life adventure game" and our hint policy is to give a hint when we see the players are stuck and/or the maximum time to solve that puzzle is reached. We can (must) know the maximum time for every puzzle because there will be another session beginning in some minutes; and we can know the players are stuck because we can see and hear them thinking out loud.

The way I would translate both things to adventure games is, first of all, being able to detect behaviors that show the player is stuck. For example, for every puzzle we should assign two or three wrong (but kind of logical and related with the problem) actions. If the player tries them over and over, we will know he is in the good path but he is stubborn with that, so it may be time for a hint. Having a maximum time for completing the game is not the way adventure games work, but... why not? We could ask at the beginning how much time the player wants to be spending in the game (based on some empirical tests): 5 hours, 15 hours, 30 hours? It's like a difficulty level and probably it should be translated to Easy, Medium or Hard to the player, but it gives the designer this new tool: Medium means 15 hours and these three puzzles should have been completed by now, so let's choose the one with more wrong actions and let's give the player a hint and wait a time before giving him another one. The goal of a hint is to make the player think that the idea has been his and make him feel smart and not stupid, so hints should have at least three levels of precision: the first time the player gets a hint it's just an innuendo, the next one it will be a clue and the last one a funny sentence telling exactly what to do (always with a time between them). Hints should be also discreet, maybe some added lines in a dialogue tree appearing at the right time instead of a big sign filling the whole screen.

There is also the information given to the player before the hint and even before the puzzle. A character says something the player should know to solve the puzzle (this makes the puzzle fair). The designer could adjust the amount of previous info given to him instead of using hints later.

Using these two approaches will make the game funny to newbies and pro gamers (Extreme level means no hints at all), because hints will only appear when needed and in a natural way that makes them look not like a hint but a part of the game and the game will have the right length for every kind of player.

Some of this could be applied to bosses.

I'm not huge into RPGs either, but I relished every moment of Mario and Luigi's Superstar Saga for the Gameboy Advance, until I got to this one boss I just couldn't beat, and that just ended it for me.  I love the Mulligan idea!

I don't like boss fights in general, it always annoys me. I also dislike "jump and run" elements in First Person Shooters or randomly respawning enemies. Puzzles in adventure games should be logical and yes, hints are always welcome - I want to have a good time and enjoy a good story and the atmosphere of the game. If I want to be frustrated or grind my way through something, I can always have that at work. But unfortunately, most game designers don't seem to understand that anymore...

I'm all up for hint systems and tips for beating a challenging part of a game. But based on what I've seen in younger kids, they don't bother. They search for the playthrough on Youtube. I wish there were a larger study and survey to accurately see the trend of difficulty and what players do when they are stuck.

I like to think of games as stories. Adventure games, moreover so. I guess I've started with a couple of obvious statements, but what I mean is...the experience of the gamer is better when the story moves along, of course those little(and not so little) accomplishments of unlocking parts and solving puzzles are damn satisfying, but they might become a painful thing once you get "stuck".
I 100% agree with Travis. As a kid, it was challenging and a 20hr game would last months (so what? right?), and even at school or with neighbors, one would "stop" people from telling how to solve that fn' puzzle.
As an adult...patience runs low, nostalgia runs high...so moving on with the game is essential!!!
I hesitated and refrained myself from calling the hint-line in Thimbleweed Park for a while (dunno what I was expecting after not playing adventure games for years, and dunno why I stopped playing them in the first place....oh yes...time) but I ended up calling a couple times that ended up being more than a couple, and I don't need to wash myself constantly nor I feel dirty about it. There I said it. I called the hint-line.
If and when the story is good...very good....great...awesome.....you crave for it. 
Like a book you read and has you glued to the sit, or has you completing the everyday tasks in autopilot-mode, because you can't wait to open the book again. 
Now it's happening with TV series. We're in an era where series are "binge watched", and that shows that the importance of completing the story go over the personal pride of not calling the damn hint-line...or solving the game with "no help".
BTW: The design of the hint-line in TWP is outstanding. The fact that it doesn't spoil anything right away, but merely starts by telling you "something with..." and ends up by either confirming what you thought (but thought you're too crazy, or thought that the developers wouldn't think you'd thought what you thought...alright, it's getting weird now) or denying it altogether, but has you saying "Oh, right!!!...why didn't I think of that?"
What I mean by all the crap above is 1) It's all about the story and the characters it 2) A little hint doesn't hurt!