Personally I preferred my lot to use dummies, which they did and gave up without any problems.
My main concern about thumbs was having been an avid thumb sucker for 14 years! - I caused a lot of problems with my teeth - a overbite which after braces/teeth removed still isn't right - my jaw is misshapened slightly.
Due to my avid thumbsucking - I needed 5 teeth removing as I had overcrowding caused by narrowing of the mouth roof.
I can remember vividly being shouted at by the orthodontist that I must give up thumbsucking. My mum had tried for years and years in the past - mustard/Stop N Grow stuff/bandages round my thumb etc.
In the end I only gave up thumbsucking when I had my brace put in - a fixed brace on the bottom with a removable plate at the top. I suffered constantly from mouth ulcers - and every month needed to go have the things tightened which in turn caused me great pain.
I always vowed that I would give my children dummies after all that - because that way I could restrict their usage. Even from babies they were only allowed them at night.
Now they are 3, 5 and 7 and none of them suck anything - dummies are well gone now and they have never had the instinct to suck their thumbs.