I'm pretty sure we should retain them, although they are not required as often.

The problem is that beyond a certain width it becomes infeasible for the eye to correctly jump back to the start of a line. There's some research on this, but I can't find it at the moment.

Smaller screens obviate the need for this, some of the time. But I've seen a lot of layouts which just compensate using white space - that fits with current design trends, but tends to mean I have a 27-inch monitor with a strip of content down the middle. It looks clean and minimal, but I suspect columnar text will come back into vogue at some point, and offer greater information density.