I'm not a huge fan of the isekai genre, but that doesn't mean I hate it either; its ubiquity is what makes me wonder why people don't just make straight up fantasy anime.
Frieren for example would be terrible if Frieren was actually some random person from earth who got sent into her setting (or, as Frieren's whole thing is outliving her comrades, her purple haired protege was the isekai'd protagonist); I understand how the isekai nature of an anime can also affect the anime, for example a character who has modern world knowledge he applies in the setting, or modern world tech, but if he just becomes a part of it, and NOTHING from his real life has any impact on the setting....then what's the point?
Overlord for example (which I didn't enjoy to be honest; I googled if he ever faces a challenge and nope, entire series and he has zero things that can challenge him) would not have been affected if he was just some lich who woke up a thousand/hundred years later.
Konosuba benefits from the isekai genre in that the isekai elements keep being relevant throughout (Spoilers:
spoiler
for example that guy who chose to reincarnate into the world with a powerful sword that Kazuma stole, or Kazuma dying and Aqua's replacement reviving him repeatedly, or that the demon lords at some point realized all their most annoying hero enemies keep starting in this one town and so decide to attack it, or that ancient scientist who turns out to be have been an isekai'd hero who creates stuff inspired by stuff he was a fan of
Most isekai animes today just seem to be wish fulfillment harem animes, which are a problem on their own as well, but they're paired with being isekais too (if you're wondering why I didn't make a thread on wish fulfillment harem animes, it's cause by and large I avoid them like the plague).
There are some interesting POST isekai stories that I found fascinating, stories where the characters came back from the isekai world and had their powers with them; in one case some of the heroes become devastatingly powerful villains who destroy entire cities, in another case it's a comedy about some guy who comes back and....could have been funnier without the ecchi/SA nonsense happening throughout.
Animes like SAO (which I didn't find interesting beyond the first story) make the other world an entirely false world and never let you forget the characters are real people who can actually die in the real world (sort of an anti-isekai genre).
In general, if they're not going to benefit from being isekai....then just make them normal fantasy. So many good fantasy animes out there that would have been hurt by making the protagonist just an isekai'd character.
Actually it is and that's a big plot element. People start to lose elements of themselves and their memories when they die, iirc like "xp loss" but their memories and shit
Actually "are there other players here" is still like the over arching plot but as of what anime has been out, it still hasn't gotten around to it
A Wild Last Boss Appears is basically trans fem overlord but it gets to "are there other players" like 8 episodes in
On that note, it being an isekai matters, in that literally the MC being inserted into "his character's" reincarnation in the other world is part of a yet to be elaborated on plan by that world's goddess to fuck up the real Lufas's plans to fuck with her. He's really in the body of the real Lufas, with her memories becoming part of his, and he realizes that his reincarnation as her is a weapon against her
I do know that and also about the horde of players committing suicide by respawn on Log Horizon. It's just that so much of the story is built around the construction of a society of MMO players and MMO avatars that I focused on the slavery episode much more so than on the memory loss side plot.
I'll be honest, I stopped watching Overlord after Season 1 because by the time Season 2 was a thing I had moved on. But I do stand by what I said though. By the same token as before, the story isn't about being displaced to another world. This Scheme, as you described it, could have involved anybody in the world really.