The safety record of roundabouts is great (almost no fatalities in roundabouts, radically safer than traffic signals), but a drawback is that they’re not very user friendly for bicyclists or pedestrians.
Pedestrians are generally forced to walk further in a roundabout versus a traffic signal because they have to walk all of the way around plus they don’t get a walk indication giving them the right of way over cars. Bicyclists need to dive into the roundabout – doable on a single lane roundabout, but harrowing on a multi-lane roundabout (or they can act as pedestrians and walk their bike around).
One of the first multi-lane roundabouts (I think actually the first) in Minnesota even put tunnels underneath it to separate bikes/peds from traffic (Radio Drive roundabout in Woodbury).
The Dutch built a separated bicycle trail outside of the roundabout where vehicles need to yield to the bicyclists – see video below. I read about this on Bicycle Dutch. I don’t think adding a bike lane to every roundabout should become standard practice, but it is something we should all keep in the back of our mind if we have a bike trail coming into a roundabout or if we think there will be heavy bicycle commuter traffic at a multi-lane roundabout.