It seems intuitively obvious that maintaining an awareness of the area behind the bike will contribute to better avoidance of (or preparedness for) developing dangerous situations, and thus to rider safety.
So here are some notes on mirrors and why YOU should have one on your bike.
The check through the armpit is only possible from the dropped position, and with the predominance of mountainbike and city-bike styles, is scarcely used any more. The more difficult movement is used, if any checks behind are made at all.
Because so much of the body is involved in such checking, checking is an effort. This means that checks will tend to be made only when the rider feels they are necessary, such as when preparing to manouevre. They will not be used to maintain ongoing awareness. More reliance is placed on peripheral vision (i.e, the degree of body and neck twist is reduced) and on other senses such as hearing. Neither of these is nearly as effective as a clear view.
The longer a check takes, the greater the risk that a problem will develop somewhere else, and the rider will have less time to note it and less time to react to it. With checks involving large body movements, the riders attention is focussed inwards (on retaining balance etc) as well as on the check itself. This reduces the effectiveness of the check.
On a recumbent bicycle, the motion needed to look behind, rather than to the side, is even more extreme, typically requiring the body to be lifted from the back-support prior to twisting.
That said, maybe someone wants to. In that case, I hope they read this first :-)
Firstly, don't mandate that a mirror be fitted to the bicycle, because many mirrors are designed to be worn on the person: Helmet-mounted, glasses-mounted, wrist-mounted. Secondly, don't mandate that a mirror be fixed to any particular part of a bicycle, as bicycles come in some very strange forms these days, particularly recumbents. Mandate instead that a suitable rear vision mirror be worn or mounted effectively, and that mirrors being worn must be able to be used without reducing steering effectiveness.
Use of a helmet mirror takes perseverance to learn, and a helmet mirror is relatively inconvenient (it breaks off, needs frequent adjustment, you need to have the helmet on at all times, it obstructs helmet covers and so on). Once learned, however, they are extremely effective, being essentially vibration-free and having an extremely wide field of rearward vision. They should be acceptable as satisfying any legal requirement for a rear-vision mirror.
Wrist-mounted mirrors are very good in terms of field of rearward vision, but are slow to deploy (meaning a longer period of distraction for the rider) and result in some weight shift. On bicycles where the hands are used for steering, wrist-mounted mirrors require removal of one hand from the handlebar. They cannot be used while indicating a turn to the side the mirror is worn on, and take quite some perseverance to learn to use. They should not be acceptable, or at least not as the only rear vision system.
Cameras have been used in some closed-capsule bicyles; they display a *non-reversed* image of the area behind the bicycle, which also takes some getting used to. I would suggest requiring that any rear-vision system display a left-right reversed image to the rider.
The size of a rear-vision mirror is also important, as is vibration resistance. If I was mandating these things, I would demand a rigid mount and a minimum size for bike-mounted mirrors.