Even in gridded streets roundabout are indeed useful. They do not have to be large. where two small residential streets cross here in Melbourne, a small roundabout only a few metres across might be installed. It eases traffic flow considerably. In LA where two streets crossed, one would have stop or give way/yield signs on both its arms and the other would flow freely. Or sometimes all 4 arms of the intersection would have stop signs. In LA this meant the first car to the intersection had right of way. Here in Australia 4 arms with stop signs means the first car gets right of way then everything behind him also, with everyone else giving way to the right.
But by adding a roundabout, it allows everyone to slow, and go round, coming off where they want. No more cars turning right blocking lanes when they give way to through traffic.

Roundabouts are traffic calming measures and might be large ones used where major roads meet, like in the posted pictures, or just small ones on fairly quiet local streets requiring no more room than the streets already used before the roundabout was built.

I recall someone in LA mentioning California didn't have roundabouts for some legal reason: fear of crashes when people couldn't use them properly, and so the city didn't want the liability.

I believe in France, ie Arc de Triomphe, the roundabout traffic gives way to incoming traffic. Hence the infamous gridlocks there.

Here in Australia/NZ, incoming gives way on the right to traffic on the roundabout, just as at any other intersection.

I've seen roundabouts that are no more than a tyre size in diameter (one, in Malaysia i think, was just that: a tyre around a pole in the middle of the intersection, more of a fender/bumper for the pole, than a roundabout!