On occasion, here and there, I have used the 1:1 aspect ratio on my Fujifilm X100F, which I have owned for a few years now. It's a lovely camera and using the square, 1:1 ratio, was just a way of exploring different settings without any idea to use or print the images.
For a long time I have been a fan of Vivian Maier, an American street photographer whose work I can just stare at and admire, page after page. She primarily used Rolleiflex cameras that produced 1:1 aspect ratio (6cm x 6cm) photographs.
This, I must point out, is in no way my attempt to produce photographs as good or similar to Vivian Maier's work – I would think that impossible, her work is so sublime. I just find it quite natural to see images and frame up photographs using the 1:1 ratio. I don't see it overriding all my work, it's just very rewarding to have the camera all set up and ready to go when the moment presents itself.