The use of "shift" as a description of an undergarment was common from the Middle Ages up until the 1800s. It was Gabrielle Chanel that first popularised the "Shift Dress", that was starting to take off in the 1920s and yes, this was absolutely based on ease of wear, moving away from corsets and elaborate undergarments and embellishments and clothing that restricted movement. Chanel began her work designing and constructing sports wear that suited a more active lifestyle. The popularity waned but there was another move towards more functional fashion for women in the 60s, and the Shift Dress enjoyed a resurgence at the same time as the rise of the Second Wave of Feminism.
There's actually a lot of etymological evidence from the time (newspapers, journals, cine reels, personal letters) that supports the idea people linked the term "Shift Dress" with the "shift" towards both more functional fashion (both in the 20s and the 60s), the "shift" in perspective towards women and references to what I previously mentioned as the ability to "shift about"/easily move in the dresses.
My original statement was not untrue. That being said, my Scottish MIL still refers to full length slips and chemises as "shifts" and I completely accept that there is a school of thought that links the 20s/60s "Shift Dress" to the "Shift" undergarment and for some people, even dressmakers and designers, it's the only explanation for the name that they will accept.
The true "shift" undergarment was quite different from the shift dress or indeed the modern day slip. I'll admit I've made a few shift's to sleep in...they're perfect for hot weather!
Also, sorry if I'm coming across as snarky or patronising as I don't intend to me...I'm ND and this is one of my specialist interest areas (in fact, I lead a module on it at the university I work at...so I can get passionate about it lol.)