Is there an inherent problem with expanding chainring drives such as Veridrive and WaveTrans? The Veridrive is just the latest iteration of the idea of using an expanding or contracting chainring rather than a derailleur for shifting:


                
            

There also WaveTrans:


                
            

We've seen this design tried before (Linley &amp; Biggs' Protean Gear in 1896). What are the problems with these types of systems that make their mass implementation doubtful? On the surface, they seem simpler than epicyclical (planetary) gear systems such as internal geared hubs and cranks.
Yes, there are problems.

Not only do the mechanisms have to be complex, as you can see in the videos, but they have to be very strong, too. The moving parts of the chainring drive has to withstand the total force the rider is delivering, because the input to the pedals will try to drive the expanding elements inwards. Complicated precision mechanisms, high strength, and low weight is a combination that is rarely found together for reasonable prices.

Compare that to a derailleur system. In a derailleur based drivetrain, the derailleur doesn't see any significant loads. All it really has to do is to move the chain from side to side. That's about it. It can be a little tricky when you are shifting under load, but pins and ramps on chainrings and cogs can do the job to ease the load on the derailleur. 

In the expanding chainrings, that has to bear the brunt of the entire rider's power output. 

Ever had a brake cable slip through the binding bolt while braking? That was only with hand power. Imagine standing on the brake lever, imagine how much of a hassle it would be to make that connection rigid enough. Furthermore, imagine trying to shift under load when you have to overcome the force you're putting to the pedals.

You still need a chain tensioner on the drivetrain too with these systems so there really isn't any benefit apart from novelty.