For cyclists, this is mostly true IMO (depending on implementation), but for pedestrians roudabouts are way better than traffic lights. In the absence of lights, pedestrians have right of way on crossing, so no waiting time, and physically slowed traffic make it safer.
This is ignorant texbook thinking.
As a pedestrian it's far easier to safely time a light, even one without a cross signal, than it is to cross through the un-broken streams of traffic that are entering/exiting a roundabout. You basically have to cross a ways back from the roundabout where the traffic is more like "just crossing a normal road". Which sucks if it's 4-lanes or really busy or fast or there's no sidewalk provision for that (like in the case of roundabouts at highway ramps) and is just a lot more walking to begin with.
For roundabouts that wouldn't be deserving of a light (i.e. the ones replacing 2/4way stops) it's a lateral move.
In the real world, drivers frequently do not stop in the presence of pedestrians.
Especially with heavy traffic, the traffic all slows down, a lot, from the section before the roundabout. Everyone is always in a hurry, so likely 10-25 MPH over the recommended speed (not the speed limit) for the roundabout, and all of them are at a 6 foot following distance.
You are playing with death to step into that. It's no joke. You end up effectively waiting for the upstream light to turn red so traffic can clear and you can cross.
The only solution I've thought of is to put a large grocery cart full of paint buckets at the roundabout for pedestrians to push into the crosswalk without risking their own lives.
I mean, it depends on your standards for roundabout. We didn't put highways through town centres so largely highway ramps and pedestrians are mutually exclusive scenarios here. Where pedestrian crossings exist, there's usually (a) an island and (b) 2 lanes prior to the island, splitting to 4 lanes either where the traffic is already slowed or past the island, which makes it much more pleasant than crossing at an equivalent junction. Also as a driver, it means you've cleared the pedestrian area before you have to consider/deal with the cross direction drivers as there's a small waiting area post-pedestrian-crossing/pre-roundabout.
If you're stuck because you already have a highway in your urban core and need pedestrians to safely cross the highway, then you are pretty much limited to overpasses and underpasses.