Yuccas in your case ,aloifolia can grow to big as a tree. Ive been to barcelona and have found it to grow there quite nicely.
The thing you have to bear in mind is that cutting each stem down means that it could branch more, or it could take on a new shape. Yuccas can respond quite variably to pruning
So, maybe, instead of pruning the whole foliage, it would be more sensible to remove some of the heads?
I would thin it out maybe, removing the side offshoots first(those that lean outwards from the plant), and then ease up the central rosettes(remove one or two in between).
Pretty much all yuccas can get a interesting shape if you prune properly. This a photo of the same species as yours, from mont juic .
Considering what other users have posted, if you want a thicker, more striking plant, probably for the best is to make it less branched/bushy and more columnar.