Why do we need gelatin in our stocks?
Gelatin is naturally occurring in meat and poultry, it's broken down collagen, which is the material that distributes force throughout the muscle. You couldn't actually get rid of it easily even if you wanted to, so it isn't necessarily that you want it, but that it is there. Reducing the stock until it is gelatinous simply means that you've gotten rid of most of the water, concentrating the stock so it takes less space, which is generally desirable. 

Gelatine and other thickeners increase a liquid's viscosity, making it coat things better, which is good for mouth feel. Most of the time that's what you want for a good dish.