Only if you're in a car. For cyclists they're far more dangerous than traffic lights (where you can do a hook turn), and also pedestrians (you can install pedestrian lights, and the cars will be going slower anyway).
It depends a lot on the design of the roundabout. Our traditional medium-sized model here in the UK, with two or three lanes coming in as one block from feeder roads, certainly isn't great for cyclists. However, we seem to be moving towards a more continental style, where for a medium-sized four-road roundabout you'd have one lane peeling off to the "first exit" and a physically separated lane onto the roundabout for those going further round.
This is generally an improvement for everyone, because you only ever have to worry about merging with traffic from one other lane at once. It's also an improvement for cyclists in particular, because you can construct those single lanes so that either they are wide enough to pass a cyclist with a good clearance or they are narrow enough that overtaking is clearly not an option. When there are several adjacent lanes, an aggressive driver will often force a cyclist into the next lane over (even if there's another vehicle there). When doing so requires driving through solid concrete lane dividers, funnily enough it doesn't happen so often...
It doesn't help when making right hand turns* or going straight. In that case, a cyclist has to cut in front of two lanes of traffic (left and straight/right), which isn't very good for either them or the cars.
You also have to consider that the cyclist needs to give way to the traffic from the right. If they've stopped, they need an extra large gap in the cross traffic, since acceleration on a bike isn't quite as good.
* - This is for areas where you drive on the left, obviously.
The risks you describe are all true, but mostly apply at traffic lights as well: a cyclist still has to navigate into the right-hand lane at a junction if turning right from a two-lane (or more) entry road.
In practice, modern design practice for roundabouts ends any separate cycle lanes well before entrances to the roundabout, thus allowing everyone to merge on approach in plenty of time. Also, the roundabout itself should be designed to limit both the number of potential points of conflict and the speed of traffic crossing those points if shared use is expected, for example by the use of solid islands and dedicated lanes that must be chosen on approach and then followed throughout in a predetermined spiral path around the roundabout. That means cycling on such roads is usually both more efficint and safer than cycling through signal-controlled crossroads of a similar scale.
For larger roundabouts, cycling around with several lanes of traffic is rarely advisable anyway and alternative provisions will need to be made. Although dedicated cycle routes like underpasses come with their own safety concerns, particularly at night and not necessarily anything to do with traffic, most roundabouts on that scale are signal-controlled anyway these days (at least here in the UK) so a separate system of crossings to allow cyclists to move around the outside like pedestrians can be provided.
> The risks you describe are all true, but mostly apply at traffic lights as well: a cyclist still has to navigate into the right-hand lane at a junction if turning right from a two-lane (or more) entry road.
No, they don't - as a cyclist, you can do a hook turn: http://www.cyclingtipsblog.com/2009/05/the-hook-turn/. Even if this is technically illegal in your jurisdiction, I'd still do it, since it's much safer than trusting car drivers to do the right thing.
Solid islands are also dangerous, since they narrow the road and most drivers will try and push past rather than slow down to cyclist speeds. Neat fact: the handlebars on my old bike are higher than the wing mirror on a VW Golf. How do I know this? They passed me on a roundabout, and the wing mirror passed under my handlebars. Lucky I ride a bike with flat bars, and not a racer.
May I ask where you cycle? What you're describing is very different to my experience here in Cambridge, and I can honestly say that I have never seen any cyclist of any standard pull what you call a "hook turn" here.
Given that we have a vocal (to put it mildly) local pro-cycling campaign and there is another one down the road in London, while I'm not questioning your own experience, I am a little surprised that no-one has been talking about and promoting such an alternative cycling technique if it really is safer in general.
In fairness, drivers around here are also very familiar with and aware of cyclists. While some drivers pass too close, and some cyclists complain at any driver passing less than an absurd distance away, for the most part the two groups do actually get along. I've never had any problem waiting to turn right on a normal line in mid-junction, nor with drivers passing as close as you describe while going around a roundabout.
