We don’t refrigerate bananas. Theres no need to since the Debbie Meyer Green Bags came out ten years ago. They work great with most fruit but especially bananas. We reuse the bag a few times to cut the cost.
Some grocery stores bag up the spotty ones and sell at a reduced price, advertising that they are great for banana bread and smoothies.
I know this is unrelated, but sometimes I buy broccoli just for the stems. At my usual grocery store they’re sold in a two or three stem bunch, rather than by weight, so ditching part of them doesn’t save any money. Raw, peeled - so good. Cooked - blech. I steam the crowns and give them to the dogs with their kibble.
Bananas - if there is a ‘bad’ one in the bunch - bruised or damaged, I will pull it off and leave it behind. I’m not paying for a banana I won’t eat. Too many in a bunch - I will hunt for a smaller bunch of the perfect ripeness, rather than rip off one or two.
Mrs. Plant (v.3.0) does something with broccoli stems.
I steam them in the microwave and feed them to tropical fish and the black worms that also feed the fish. 
My husband likes to remind me about the time I was breaking a banana bunch in half at Safeway, and the other half flew out of my hand and landed about 20 feet away. He says it is one of the very few times he’s seen me blush. 