Yep, I definitely use it . It's rare because we don't talk about the situations it describes very often, but when we do talk about those situations, we have to use future perfect continuous. There's no other structure that works.
"When I get to your place tomorrow, *I'll have been driving* all day, so I'll be tired and stupid."
This sentence doesn't feel formal at all. It's a normal part of spoken language.
don't worry about it too much.
The vast majority of sentences we say are in present continuous, present simple, present perfect, past simple, and future simple.
Natives definitely use the other tenses, and they don't seem strange or formal at all. However, if you are good at using the 5 most common tenses, you can have almost any conversation you want to.