Henry did say you can get full size bulbs with scapes on, but you have to leave them quite a bit longer. So for a timely crop, removing scapes makes sense.
Also of course, they are delicious!!
If you want to grow some up from bulbils, then it's best to leave the scape on a plant until it matures. You can also dig the whole plant with scape, and hang them to cure and finish developing their bulbils. Nan, since they are dying back perhaps you should dig the bulbs and see if there's disease or damage there, or are they just drying down as their season ended? Even a cut scape can produce some bulbils if you give it time, and if you wanted to save that variety.