You're getting a lot of great feedback here. The one thing I would add is this: There is danger in focusing too much on one specific variable. I think it's dangerous to say something like "X is the most important factor in determining Y." Yes, a thinner soundboard is likely to make an instrument that sounds louder and has a more pleasing tone. But if you're aware of, and controlling, other variables as well, it's trivial to build an instrument that appears to disprove that general rule.
The top doesn't really care how thick it is (within normal uke top thicknesses). The things that really matter are the stiffness, elasticity, and mass of the top (assuming all else is the same). Those are the physical properties that influence how it vibrates (and how the vibrations decay). Thinning the top plate itself is one of many ways you can influence those three parameters. But it's not the only way, and it's probably not even the most practical way. You can change the stiffness and elastic properties by changing:
- the wood choice for the soundboard
- the bracing pattern, how the braces are carved, what wood is chosen for the braces
- size shape and species of the bridge
- size shape and species of the bridge plate
- size and position of the soundhole
- material and size for the rosette
- size, shape, and species of linings
- the type of finish
- the dish radius
- the overall shape of the body
- the size of fretboard overhang, the thickness of the fretboard, and the species of wood used for the fretboard
- the size of the tail block and neck block
And that's just the top! Not to mention the back, sides, and neck.
Ultimately, there are practical considerations as well. Generally you can make a top perform better by thinning it, but there comes a point where things go badly very quick. If the overall top structure (including the braces) is not stiff enough, it will belly under string tension. If the braces versus the top stiffness aren't well matched, the top can crown around the braces (so the bracing telegraphs through the top and the top looks wavy). Even if you manage to solve for those problems, there reaches a point at which the top may be structurally sound, but becomes so thin it can no longer pump air well (at least, within the confines of a uke body). A top that is progressively thinned will reach a point at which the tone and sustain just sort of die - it stops sounding like a fine instrument and starts to sound like the top is made from cardboard or paper or something.
And as I mentioned above, it's possible to alter other variables to get to the same goal as a thin top. This is essentially what happens to combat "I can't make my top thinner or I'll have problems." You adjust all the variables in relation to each other to account for limitations. Bracing can be altered to accommodate a top that "wants" to be a certain thickness, for instance. And so on. Building an acoustic instrument is about balance, compromise, and understanding interactions. There is never really a single "best" value for any variable, out of context of the entire design.
So, ultimately, at the end of the day, I don't think it's super appropriate to make a statement like "thin tops are better" because you really need to consider the entire package, not just the one variable. What you can safely say are things like, "thin tops are less stiff" or "thin tops have less mass."