I vastly prefer roundabouts, with a single exception. If traffic is heavy and dominated by the same entry and exit points, it can be hard to get a turn if you're coming from the side. Our nearest roundabout is this way.
I once saw a roundabout with stop signs. I assume it was an attempt to address this situation.
You do, but that means there is no roundabout when you need it the most.
The problem occurs mostly when the dominant flow is given multiple lanes.
A fairly common solution/workaround is blocking the view of the approaching traffic, forcing it to slow down. But again, this doesn't work well on large roundabouts that allow people to speed up to of 30+ mph.
I used to go to work past one like this. They replaced a light where you would always eventually get to go with a roundabout where the 99% of traffic going north/south meant the other two ways were effectively not part of the traffic network for a few hours a day.
I once saw a roundabout with stop signs. I assume it was an attempt to address this situation.