The mainline Pokemon games are not difficult. You might even describe them as "big dumb baby games for big dumb babies." I know this because I've done and I'm a fan of the series. They're so easy most of them can be beaten by using nothing but your starter pokemon for the entire game, bar the occasional HM slave to let you get around the gameworld. This is how many younger players start off playing the games. In terms of gameplay, failure, or the threat of failure, is basically a direct result of a game's difficulty or challenge. When a game doesn't present enough challenge to create the tension of possible failure, players will often turn to nondiagetic restrictions on their gameplay to artificially insert it.
For Pokemon, one of the most popular forms of extra challenge is doing a Nuzlocke run. The Nuzlocke challenge was invented by Nick Franco in 2010, popularized by his webcomic detailing his very first run, and named after his Seedot who he drew to resemble John Locke from LOST (it died). In a Nuzlocke, there are 3 main rules. First, if a Pokemon faints, it's considered dead and must either be released or placed in a PC box, never to be removed. If all your Pokemon die, you fail the whole run. Second, the player may only catch the first Pokemon they encounter in an area. If they defeat it or it flees, they lose their chance to increase their roster. Third, all Pokemon must be given nicknames to increase the emotional bond with said Pokemon to make them less disposable. There are many potential 'clauses' a player may choose to enact in order to raise or lower the difficulty. Some examples would be a 'dupes clause' that states that you aren't bound by the catching rule if you already have a Pokemon of the same species, not enforcing the rules until the player gets their pokeballs (effectively the end of the tutorial/prologue to each game), or using the 'set' battle style (which makes it harder to consistently use advantageous Pokemon with no risk). There are also other, less common, 'clauses' can make the challenge even more lenient or severe.
What's most intriguing about the fact that the Nuzlocke challenge exists is what it says about players' relationship to failure. More than just wanting simple challenge added to their games, some players want a chance to genuinely fail. Because the 3rd rule encourages players to become attached to their team, it's clear that Nuzlocke players don't just want to lose the video game, but have chances to lose things of real (if minor) emotional weight. The next question to ask, and one that would likely take a full paper and some bonafide research, would be about how players understand failure they inflict on themselves versus how they understand failure inflicted on them by design (whether that's a punishingly difficult game or just one where failure is a near inevitable outcome like in SPENT).
William, I really like the ideas you bring up here! As I've grown older and my taste for challenge has development (and as, arguably, mainstream games have historically gotten "easier" or more forgiving in our lifetime), I also have been thinking about my relationship to failure as a player. To respond more directly to your question about self-inflicted failure (in metagame challenges) and failure inflicted by design: my first thought is may really comes down to how failure contributes to the tone and procedure of the game. I find myself interested in inflicting failure upon myself with metagame challenges (like the three-heart challenge that Lupe mentioned in Zelda games) when I'm too attached to other qualities of the game to…
I think it's cool that there is an intersection between meta-gaming and failure and how meta-gaming can make a game way harder. Setting your own rules to change the failure states and difficulty of video games is applied to games that are already hard too. This reminds me of the three hearts challenge for the Legend of Zelda games where you play the entire game with only three heart containers for health. I think of failure in terms of fun too and I think that players do challenges like this because failure in games can make them more fun.
As someone who once tried a Nuzlocke myself I think its interesting to consider constrained playthroughs as metagames. I failed my Nuzlocke run because I personally felt wrong releasing my starter pokemon after its first death. I ended up just playing through the rest of the game the regular way and had a good time with it. I met the failure condition of the metagame I created for myself