First of all bettas are carnivores. How can people expect carnivores to live off of a plant? If you are not feeding your betta at least two times a day and you expect it to eat off the plant, after about two or three weeks you'll have a dead fish. They will not eat the plant!
Second of all the plant does not help with any cycle. You will still get the same amount of ammonia in the vase and if you don't change your water you are slowly killing your betta.
And finally those vases aren't very big with not alot of surface area for your betta to breathe from.
The only time when I would be okay with this is if you are doing regular water changes, feeding 2 times daily, and keeping the roots trimmed back.
