Hey there @chbartist!
I actually think what you say would make sense in a majority of situations, but not all of them. It probably depends on how much of a bad place you are when you start and how big you want the change to be :)
If you are already quite stable little by little works, but when you are all over the place you need a big shock to kick-start.
Considering that you will for sure fall along the way,
in my case I found it to be better to really push the change till I collapse,
let go for some time, and then come back to it.
At least when I failed I did not think "Oh, I am not even able to keep up with this small step."
but instead my internal dialogue was "Well, not too bad. I failed while reaching for the moon. Let's try it again!"