I really would like to know if there is danger in this kind of setup.
I really don't think there is a danger in keeping the plant there as long as you care for it. The problem is lots of people believe that the Betta can just eat the roots and doesn't need any other source of food. Bettas are carnivores and shouldn't be expected to survive off a plant. The other problem is that people often use such tiny vases not knowing that Bettas need a good amount of room.

edit: Here's a good website about that Betta's in vases