Well the plant gets its energy to build flowers from the old fan leaves that turn into energy supplies for the flowers.
Why do those fan leaves turn yellow, IF you leave them on the plant?
The reason is this, chlorophyll (the green stuff) in the leaves is stored energy in the form of several different sugars that the leaves create during photosynthesis. The plants will later on as the leaf matures, use up that stored energy to create FLOWERS and seeds.
So by taking off all the fan leaves where does the plant now get the energy to produce flowers?
The plant "might" look to the roots but that isn't how the plant gets energy to produce flowers. It does that with photosynthesis. here's the cool part, due to the location of the fan leaves - take a look should be located right where the leaf stem meets the plant stem there's a stem shooting out right there and that new stem is where the flowers are.
So the energy goes into the fan leaf down the leaf stem then up the stem into the flower. That process is called translocation.
Roots do not create sugars the plant needs to grow flowers. This is ONLY done is the leaves.
Moving on to the fan leaf that turns yellow. This process is how the leaf gives back its stored energy to the flowers. The process is called abscission and resorption.
I'm not making this shit up. Wiki has it spelled out right here:
Be sure to read the "process"
https://en.wikipedia.org/wiki/Abscission#Resorption
That bag of fan leaves you throw (hopefully in the compost bin) is a bag of nutrients, sugars, proteins and plant hormones the plant needs to finish its life cycle. This is science not some anecdotal bs.