Anecdotally I’ve known people who’ve lost a lot of weight by cutting out soda completely. But success at the individual level can’t be generalized to the population level. Healthcare is nearly 20% of US GDP and nobody doubts obesity is a real contributor. An outright ban on soda would be infinitely more successful and if that would solve the major problem of the industry, I think you’d hear more about it.
I’ll try to put a finer point on it. You can’t (shouldn’t) just increase the cost if access to alternatives is also part of the problem. If you don’t increase the access to high quality, affordable alternatives you will just make things worse. There’s a lot of discussion in this thread that is only looking at one part of the problem (consumption of unhealthy food) and ignoring the other aspects (like access to higher quality alternatives)
From the standpoint of public health policy, it is a good idea to introduce simple measures that are effective for 90% of the target group. If it turns out necessary, you can find a (perhaps less optimal) solution for the other 10% later.