hi Davide,
I always have a small clipboard and velcro it on the back of the slate and have another binder clips on the other side.
I have been using this system for years, it works great for me. It fits with dummy slate, smart slate, mini smart slate, insert slate, or you can put it on the pouch (depends how big your pouch is).
This does not take a lot of work. I always keep velcro soft and hard side at least half foot in my pouch with fiskar scissor, it can be done in less than a min.
The system of having camera log book putting it in your pouch is way too much work and you don't have hard surface to write on.
Production gives us 3 pages(white, pink, yellow pages) of camera log, each card reload, you give one to production, one to post production/DIT, one for yourself.
I never had a DIT takes a picture of my log.