For some reason people tend to think pruning succulent stems is some sort of florist art. They ask, will the long flower stalks continue to grow with new leaves at some point, or would it better to trim them down?

If the flowers aren't as much of a concern, is it just an aesthetic choice?

You can do what you want!

I enjoy the flowers for a while and then cut the stalk off. I had one echeveria that kept sending up flower stalks, 4 total this season. I just cut the last one the other day because its December and the stalk was so big and heavy it was tilting the whole plant to the side.

In my experience, echeverias don't grow from the flower stalks.

I know some people have a lot of success propagating the leaves that grow on the flower stalk, though I don't know about the stalk itself. You can defiantly propagate the leaves from the stalk. I never let any leaves go to waste!