It's my understanding that the kick drives the roll, so even with a non-propulsive kick it's important to have a kick anyway.

> Strangely enough, my breathing was better when I was kicking less...

What do you mean by "better"? Unfortunately, kicking uses your legs muscles and they will need oxygen, requiring more/better breathing. That's why it's important to find a good balance between kicking enough to drive your roll and not kicking too much. A championship swimmer still only gets about 10% of their propulsion from their kick.