T-shirt quilts are a set of skills and talents all unto themselves. Some people love them and are awesome -- I try to avoid making them, but have because they are a great gift.
Currently, people are using t-shirts for mask making (you can make ties by cutting rounds from t-shirts), but in general, other than the logo or pocket or whatever you are keeping from the shirts, they are mostly just scrap.
The big thing is in preparing to turn your shirts into fabric, and not be concerned about what is left but what you want to use. I like to keep the shirt whole until I put on a massively oversized piece of fusible interfacing, only then do I subcut it down. The way I work, not only are the shirts 75% or more waste, but I probably cut away/trash almost as much interfacing as I use.