I create this shape of a lamp from a circle. Created the convex shape of the glass cover by curve and follow me and then off set the edge of the circle and push pull for the cover.
As @Wo3Dan wrote, the native Weld, which you show in your screenshot will weld the edges into a curve. Eneroth Auto Weld will weld them into a circle.
It is a paid extension but considering what it can do, I find the small cost more than worth the time it saves me.
I don’t know if it should happen with the Follow Me tool but it doesn’t natively. There are other things that can explode curves too. This isn’t specifically about circles either. There is other geometry that maybe needs to be welded together in some way.