I share your feeling cloudgazer. Can be very frustrating at times when riding in a group. Feels like a lot of waiting and very little riding at times. When going solo - own pace, but it is definitely safer in a group.
I dunno if it's really much safer in a group.
you may ride beyond your skills to prove a point or to keep up with the pack.
having a group around may lead to a false sense of security.
Although it is aweomse having people around to help pickup your bike when you drop it. 
I haven't really ridden in any big groups yet, not sure its something I would find enjoyable, so cant speak from experience, but my observation from reading various comments and ride reports is that I agree with you that it probably isnt safer in a group maybe even a bit more dangerous.
I think we all have a competitive part to our personalities and instead a "ride" it can become a subtle form of race in some cases. In small groups with people you know, who are at similar levels of capability, thats fine and quite enjoyable, but in large groups with a wide range of skills people might be tempted to try and show what they can do, or feel pressurised to match the pace of the hot shots, rather than just ride their own ride.
I personally prefer riding with a mate or two only. Sadly I dont have many mates who have bikes, or if they do they dont tend to ride often for some reason. So I tend mostly to ride alone. But I really like going at my own pace which varies considerably, according to my mood. I also have a firm rule of rather ride like a ninny (I'm past the age where its important to prove anything) than go back to hospital again, so when in doubt I slow right down (although as I get used to the bike my average speed has increased steadily - need to ensure it stays this side of the complacent curve!

).
Of course if you fall its great having others around to help.
And its certainly a lot more social with more people.