There were some games that had a feature called game sharing. This let you send a smaller version of the game, essentially a demo, to another PSP over wifi, and this let you at least try the experience without owning the game. Burnout Legends definitely did this, but I also remember it on some NFS and sports titles. I just found a list of games that did this.[0] Also, there were some good shooters as well, like Medal of Honor or Battlefront, with pretty nice maps, especially for a handheld. And for racing games, Gran Turismo was incredible with almost all GT5 tracks and 900+ cars present.

[0] https://www.lifewire.com/psp-games-with-gameshare-2792549

For some reason the DS didn't take off at all in the area I grew up (neither did the original Pokémon games despite seemingly being massive everywhere and the cartoon being a big hit in my school).

it was only like ten years later when I got to realise how great those download play titles must have been for some kids. PSP games would have been way too large to pull off similar stuff, DS games were often only a few megabytes

Maybe it's just because it was high school and not elementary school, but I remember basically everyone who was into games even a bit having a DS, but nobody used them as a daily carry portable. It was something you'd just notice in people's rooms when you went over.

> I don't think PSP games were capable of this.

They were. You could play Tekken against a friend without him having to own the game. It was great.

But in general not many games did this. Since even Tekken had pretty high load times, I suspect that the much higher graphical fidelity of the PSP made most games just too big for this to work well.