Old isekai had the MC want to go home. Modern isekai has the MC wanting to start over and stay in their new world. You can chart the change based on how dissolutioned young adults are about the Japanese Dream of stable employment and raising a family.

The fantastic book series Magic Kingdom For Sale is basically about this. I started reading what I assumed would be a lighthearted comedy and it literally opens with our main character lost in alcoholic depression because of an awful tragedy. The fantasy land he's sent to is hostile, but it provides him enough hope to fight for a better world there.

There's a big trend in recent isekai to just outright kill the character at the beginning. So, you're either reincarnated into another world or your soul is snatched upon death and body recreated in the other world as an explanation for why the character isn't spending their whole time just trying to get back, but I do think that would be an interesting angle to explore.

If I could bring my cat and like 3 other people, I would 100% be like "good luck, losers!" and would never be heard from again lol.

I'm aware of a few early isekai works from like the 80's to 90's (Dunbine, Elf Hunter, and quite a few western Choose Your Own Adventure books and pulp novels fall into this category). It seems to be that as a trend, the premise is that the main character wants to get back to the "real" world and that usually drives the main plot.

Then theres a big trend of Isekai light novels (and related anime etc) in the later 2000’s to today. These almost exclusively seem to feature characters who just want to live a life in their new fantasy world. Literal escapism, even. Konosuba is notable for being very popular, maybe being around the start of this trend, and the main character is given a task to complete and be returned to the real world, but he just ignores it.

I guess we can speculate on whether this means people got more miserable in the intervening time.

Sword Art Online's original premise sounded kinda fun to me tbh. Though I have a feeling the whole "society makes sure that the players get life support in the hospital while they are stuck" wouldn't work as nicely in RL as it did in the anime. But "can't log out of video game because it'll kill me if I really try" would be kinda nice for a while.

Campfire Cooking is my favorite one of the newer crop of these.

His super power is basically Amazon Grocery. He immediately hides that fact from everyone, tells the people that summoned him he's useless, and leaves the country to live "off grid".

And all that before he even knows how that world works. I'm not even sure he knew he could do other kinds of magic at that point. Natural instinct to GTFO society / authority was something I could identify with

Even the Wish-Fulfillment Isekai are pretty gritty for everyone who isn't the MC, though, so in that situation most people would probably learn to suck a john, find a way home, or die.

That's why I like villianess stories in otome isekai, it makes sense why they want to go back

I'm not sure what you mean, I don't think I've seen a single isekai protag try to go back to Earth unless you count the "trapped in VR" ones.

I'm always a little disappointed by how quickly the regular world becomes irrelevant in the story. The intrigue is from how a person from a modern nonmagical culture interacts with a medieval magical culture.

But from the isekais I've seen, I'd say you could replace half of them with a person with amnesia and nothing would change.

This trope has been explored, sure enough.

Recently, I recall the comics DIE, although I didn't finish it yet. And also the TV show The Magicians. In both cases one of the crew stays to be a king while everybody else goes home. And time runs at different rates on either sides. And then they meet again. Hijinks ensue.