Welcome jsh and good question for your first post.
Although a toothbar is not 100% necessary requirement, it is one of those items that makes using your FEL bucket a little easier ... a lot in some cases. But it has drawbacks too. I'll point out some pros and cons and I'm sure others will chime in with a lot more information.
If you are digging with your bucket, or picking shrub and sticks, the teeth help quite a bit. They allow better penetration into hard or soft dirt piles and get "under" debris like branches or sticks. This is the major plus as some digging is impossible with a good toothbar. Working with a grapple for shrub removal is wonderful. Downside is back dragging with the bucket lip now not smooth. However, you can use the rear of the bucket to do that like I do. It is removable in most cases so you would have the normal shape of your fel bucket lip back.
Most toothbars have a big thick bar that the teeth are attached to and when you put it over your bucket lip, it adds a lot of strength to the bucket from bending or bowing under pressure. Another big plus to keep your bucket in shape. Downside it's slightly heavier by a 80-100 lbs or so.
Another advantage is if you want to "pop out" small trees or shrubs or even rocks. Hook one or more of the teeth under the rock/root ball or near the bottom of the trunk and pry the tree/shrub out. This works great and fast.
Most guys would agree a toothbar is advantageous for guys who do a lot of digging and tree/shrub removal. It's also easier to a degree to get rocks sliding into the bucket. However, if your going to be spreading manure or gravel and not digging, no toothbar is needed. Then again there are a lot of guys who do all the above without one too.
?