it is not a requirement- but can be done if you want to- if your appliques are (heavy/bulky) you might want to to reduce the bulk- or if you are hand quilting you may want to- some recommend it for large pieces- so you avoid any shadowing- i've been a pretty avid appliquer for 10 years+ now---and i think once i did trim the backing away under an applique---but only once- really saw no reason to do it- i machine quilt- and like my quilts to be fairly heavy so saw no reason to reduce the weight in that way (seemed like alot of wasted time to me-with very little benifit)
some do- some don't it's a personal choice- not a rule.