It doesn't even have to be a cursor, you can technically page off of any field you can index (i've written a lot of sync APIs so there are gotchas, but the point stands).

Limit/offset is usually (though not always, as you point out) egregious for anything more than hobbies or small projects. But, I am biased as when I build APIs, I definitely expect some amount of traffic/volume/tuple count, and offset/limit will not do.