I'm sure someone with more experience can weigh in better than me. From my understanding, they are important to a degree, even outside of calligraphy, where of course they are very important.
Handwriting will start to deteriorate as people write faster and more sloppily. However, if they use the correct stroke types, it will deteriorate in a more predictable manner. I'm gonna be honest here, I do personally not pay attention to the stroke types, but for example if you look at "tome" vs. "harai", doing stop pen -> lift pen means it's way less likely for there to be a faint line from the end of one stroke to the start of the next one, as would often happen after sloppily writing a "harai" stroke.
This is the same reason why stroke order (and direction) is very important when it comes to legibility of handwriting.