I can’t say I advocate either the cold turkey method over the using incremental change for all life changes. My best answer would be to terminate old habits with the cold turkey method and build new habits using incremental change.
Whenever I quit smoking or something like that, I need to completely stop because I’ll “fool” myself into thinking I’m quitting, or keep telling myself that I’m just going to do something for one last time…and I’ll tell myself this multiple times and generally end up somewhere worse than where I started from.
As for building new habits, I either jump in feet first and burn myself out after a couple weeks, so instead, I try to slowly and carefully add new things to my life. For instance, I’m slowly mixing new healthy habits into my day. I’m trying to get as much water as I need, as well as maintaining a little bit of exercise, just to strengthen my leg and get in the habit of exercising.