A handwritten letter was often how others got their first impression of you, so you had external motivation for caring about it.
Now i feel bad for my colleagues who were diligent students and learned cursive. They are stuck with handwriting that becomes increasingly illegible to the general population with every passing year. The only benefit it offers is being marginally faster than printing, but still vastly slower than typing. People are so used to reading print that i would argue cursive is becoming regarded as somewhat unprofessional.
Are younger people really not able to read cursive? I find that hard to believe; it's still the same letters.
Sure, we type often and so write much less than we used to, but most of us still write on occasion, so writing must still be taught.