Do the benefits of clipless pedals out weigh any danger they may pose the rider? As a newbie rider, I was asked by many experienced riders and bike shop experts if I was using clipless pedals yet?  The implication was you are not really a serious rider until you are clipless, sort of a rite of passage. No one ever told me you can break bones, but told 'everyone' falls a few times, count on it, and move on. 

Are there precautions or conditions where one could or should not use clipless pedal products?

The previous year, I had ridden 1700 street and paved bike trail miles on a comfort bike and a Mountain tandem with Pedal Cages and never had an issue.  I incorrectly assumed I was ready to advance.  I purchased a new touring bike with Shimano M540's.  

Here is an XRAY of the damage I experienced riding clipless.  It was an unexpected stop due to a flood closing a tame paved trail. Someone had painted a bright blue line from the trail up to where I fell (me standing in the picture).  It was my error in trying to ride around the obstacle and ended in the railroad ballast (2"-3").  I had un-cliped going up but the M540's re-clipped  I stopped at the edge of the ballast but was clipped.  My ankle twisted > 150 degrees. It was my third ride and fall clipless. It all happened in 10-15 seconds.

I know through good friends of two very much younger but very experienced  riders who were hurt much more severely than I due to clipless.

Should I try again with the beginner clips and different pedals, or as my son and wife tell me, are you crazy?

Revisited

Having just rolled over 2,000 miles this year with flat pedals on the road I can report I have found a solid solution for me.  I now ride with "Pin" Pedals available from several manufacturers I use (Xpedo MX Force 3).  These pedals have a grid work of short pins sticking up on both sides of the flat pedals. These pins rather lock my foot on the pedal preventing foot creep or shifting out of position while allowing for quick mount and dismounting as necessary.
Terminology is important here. Pedal Clips (refer here) are straps that tighten around the shoe. Clipless, such as SPD have a cleat - refer here
Toe clips are not common these days - but still used by some (touring and fixed hub bikes) more niche applications. I assume you are talking about SPD style clipless pedals, but the following discussion does not really change if you are using clips. I do not believe they are dangerous. However, there is a learning curve - it's similar to asking &quot;Is learning to ride  a bike dangerous&quot;, in that you will get exactly the same answer. Do it in the right locations and take appropriate precautions, expect a few skinned knees and at very worst, a broken bone. Do it in the wrong location at the wrong time, at worst - death.
What precautions - learn to use them in the same place you would teach a person to ride a bike. Avoid heavy traffic - no point falling under a B-Train - and mountain trails with large cliffs along side the track until proficient (Unless you are wearing a parachute) . i.e. Use common sense. Practice clipping and unclipping - and don't venture too far from your safe area until you can do both without looking down (If you look down at you feet, you will fall off). Then - practice &quot;emergecy exits&quot; - Not needed so much for onroad riding, but MTBing, you often need to unclip without expecting it. Eventually you will be able to unclip at any time, without thinking about it.
Don't use mix the use of toe clips and clipless pedals - it will end in tears, as the exit methods used for of each is completely incompatible with exiting the other.
Where not use them - anytime a fast, unhindered separation between the bike and rider is likely to be needed - BMX, Downhill MTB and Trials riding come to mind. In some XC riding, it is advisable not to clip for some sections - depending on the riders confidence and competence, however most of the time an XC rider will be clipped in.
Some riders prefer flats - especially MTB - there is nothing wrong with that - don't feel forced into using clipless pedals.
Edit:
Updated in response to comments.
In response to you photo and attached picture - not an entirely unexpected outcome of a novice to SPDs riding rocky ground, as might be expected putting a novice bike rider on same ground.  Unfortunately you now have an additional couple of problems to overcome if you decide to go with SPD's. You will have a mental aversion to them, and to rocky ground - that needs work but is relatively easy to overcome compared to the other - If you go with SPD's your wife will be certain you are mad - nothing you do will change her mind on that....
I suggest not using beginner clips  - they will install a false sense of security &quot;I'm on beginner clips, I can un-clip easily....&quot;.
However, there is absolutely nothing wrong with flats.....