The problem with a full sized or even a trim router, is the size and weight. It is very difficult to route a decorative edge on small items. Even if you are using 1/4 shank bits, they are often too large for 1/4" and 1/2" stock. Forget about anything smaller. I don't use that plastic insert either. I believe it is a safety thing. I'd have to pull out the instructions. I won't use my big router table for these tiny pieces either - I like my fingers too much.
The piece moving around, as shown on the video, is pretty easy to remedy. I use thick, woven foam shelf liners. That usually keeps them in place. On bigger pieces that I am using a bigger router on, I use Bench Cookies to elevate it and keep it in place.