I only iron what I need for a project.
Wash and starch and dry fabric
fold it selvage edges together and straightened
when a quilt calls for 3/4yd I pull it from my stash and cut that amount off my yardage
I only press that amount. If it is a little wrinkled a spritz of water helps.
I don't find very many wrinkle problems doing it this way. I don't like pressing fabric and storing it, pulling it out to use and pressing it again, that would be torture for me.