Its not a free lunch. Statics are prone to be hard to string compared to most working recurves. However with a little practice and a good block stringer that is not an insurmountable problem. Statics require greater torsional stability which can be tricky , especially in the lower weights.
The need is generated because the tip does not bend with the rest of the limb so it is critical to have great torsional stability . How this is achieved directly effects the efficiency and overall performance of the bow. It is why I personally prefer the static to be accomplished with very little additional weight if any. Geometry , hense my coining geometric static as a type, is the best way to accomplish this as it it not necessery to add any weight. No heavy overlays or wedges. The materials you use in the bow limb also have a lot to do with the static design working properly. length of working limb, height of recurve to notch,ect.
A good amount of help can be hade with 45 45 weave carbon or glass added to the stack to give torsional stability plus belly strength, however that is accomplished it contributes to the bows stability and performance.
A strong belly adds a lot to torsional stability.
Sooooooooooo, To answer , are they a free lunch? Not unless the bow is extremely well designed. Then I see absolutely no down side.
God bless, Steve