My handwriting has turned into a mix of block letters and cursive over the years, and has become increasingly less legible since it is so rare that I actually write anything that isn't typed. I don't really have a consistent signature anymore.
My understanding is that cursive learned in school is supposed to be a launching point for your own style of script. I.e. you learn the fundamentals and then you learn the shortcuts.
I worked in a paper-heavy environment where quick and dirty writing was important to adopt in order to get stuff done.
Besides faster writing, children also learn fine motor skills by practicing different forms of handwriting. We had cursive in third and fourth grade and half-uncial calligraphy in fifth grade, not because we were expected to illuminate manuscripts but because it gave us time to learn how to control our hands.