Would variable crank arm length be beneficial to a rider? I was thinking it would be cool to have a bike where the crank arms can be adjusted automatically "on the fly", depending on load.  If that is not  so safe then maybe a manual adjustment that the rider could make from a control mounted on the handlebars while riding.  For example, when extra torque is needed, the crank arms could be extended to maybe 180mm.  When cruising along on flat pavement on a windless day (or with wind at the riders back), shorter crank arms might be desirable to save on excessive leg motion.  Having adjustable crank arm lengths might actually extended the effective gear range even wider.  For example, suppose the crank arm length adjustment is between 180mm and 140mm and is currently set in the mid portion of 160mm.  The rider then attempts to ride up one of those spiral walkways that are part of a pedestrian bridge over a roadway.  If the lowest gear has already been selected but more hill climbing torque is needed, extending the crank arms from 160mm to 180mm should help.  Even if 180mm is excessively long for the rider, it is only temporary until they crest the hill, then they can be reset back to 160mm.  I think that would be another fun thing to play with on a bike.

So my question is would this be beneficial to a rider and if so, why don't I see these available?  Has anyone attempted to make this, either homemade or available to the general public?  From an Engineering viewpoint, can it be done?  If so, how?
The system you propose is just a third way to change gear, in a mechanically very complicated way. Any benefit that could be obtained by lengthening the cranks can already be obtained by moving to an easier gear and a bike with two or even three front chain rings and anywhere between five and eleven rear sprockets has plenty enough gear ratios available to cover all situations. And if the range of gears available isn't wide enough, replacing the chainrings and/or rear cassette is a much simpler fix.