Bromeliads

I tried separating pups on a fascicularia some years ago. It did not go well...
But I had previously left the mother plant grow into a group, and so I think the roots were just too entwined. Your situation is nice and clean. With a big group, they do not all flower at the same time.

 

Yes I have found you need roots attached to all divisions, its very easy to end up with all the roots attached to one section.