I think it'll turn out to be a okay plot point, once we find out what the origin of the various illnesses are.
And I do think all these diseases will turn out to be somewhat linked. I think Roger's disease, Whitebeard's disease, Amber Lead, Tree Fever, Sapphire Scale, and maybe a few others will probably all come from a common source.
And my personal bet is that "common source" will be because this entire planet is basically a mass grave.
All these diseases seem to either come from underground like Amber Lead, or from trees which have their roots underground. So, I think that the First World's Underground Mining Operation has some ties to all these diseases. Probably because there's a lot of dead and/or frozen bodies at the center of the planet.
Being around any sort of decay or rotting flesh is usually not too good for your health. If the entire planet is basically built on top of a mass grave, it's actually kind of a miracle that more people aren't sick. Maybe all the water is actually working as a sort of "barrier", keeping most of the germs and bacteria underground, and away from most people. As long as they don't get too close to the Underworld underground.
Chances are, Laugh Tale has some sort of tunnel or elevator that leads down to the center of the planet. Some sort of entrance to the Underworld. And that's probably where Roger picked up his disease. Whitebeard I'm less sure about, but maybe he's more connected to the planet, just by virtue of having the Earthquake Fruit. If the "planet" is sick, maybe he's sick too? That's a stretch, but maybe opening up more fissures to the underground just exposed him to more underground gasses and germs? There's a few options here.
I think the diseases subplot kind of works, if only because it works as a "great equalizer". It doesn't matter how strong you are, if you cach the wrong disease, you could end up dying. There's a factor of luck to it all that kind of works well with some of One Piece's grander themes. There's a level of tragic irony to it that I think works with backstories in One Piece.
So, I think the disease plotline will end up making more sense, once we get further into the story. We'll probably get some backstory that explains it, which will connect to some of the larger mysteries of the One Piece World. If I'm right, it should be a interesting reveal, all things considered.
