I'm starting to feel I don't know what's being meant by uncertainty here. It is not, to me, a reason in and of itself either way - to push the button or not. And not being a reason to do one thing or another, I find myself confused at the idea of looking for "reasons other than uncertainty". (Or did I misunderstand that part of your post?) For me it's just a thing I have to reason in the presence of, a fault line to be aware of and to be minimized to the best of my ability when making predictions.
For the other point, here's some direct disclosure about why I think what I think:
There's plenty of historical precedent for conflict over resources, and a biological immortality pill/button would do nothing to fix the underlying causes behind that phenomenon. One notable source of trouble would be the non-negligible desire people have to produce offspring. So, assuming no fundamental, species-wide changes in how people behave, if there were to be a significant drop in the global death rate, population would spike and resources would rapidly grow scarcer, leading to increased tensions, more and bloodier conflicts, accelerated erosion, etc.
To avoid the previous point, the newfound immortality would need to be balanced out by some other means. Restrictions on people's rights to breed would be difficult to sell to the public and equally difficult to enforce. Again, it seems to me that the expectation that such restrictions would be policed successfully assumes more than the expectation for those restrictions to fail.
Am I misusing the Razor when I use it to back these claims?
Perhaps I confused the issue by introducing the word "uncertainty." I'm happy to drop that word.
You started out by saying "The reason why perhaps not push the button: unforeseeable (?) unintended consequences." My point is that there are unforeseen unintended consequences both to pushing and not-pushing the button, and therefore the existence of those consequences is not a reason to do either.
You are now arguing, instead, that the reason to not-push the button is that the expected consequences of pushing it are poor. You don't actually ...
I might need a better title (It has now been updated), but here goes, anyway:
I've been considering this for a while now. Suppose we reach a point where we can live for centuries, maybe even millenia, then how do we balance? Even assuming we're as efficient as possible, there's a limit for how much resources we can have, meaning an artificial limit at the amount of people that could exist at any given moment even if we explore what we can of the galaxy and use any avaliable resource. There would have to be roughly the same rate of births and deaths in a stable population.
How would this be achieved? Somehow limiting lifespan, or children, assuming it's available to a majority? Or would this lead to a genespliced, technologically augmented and essentially immortal elite that the poor, unaugmented ones would have no chance of measuring up to? I'm sorry if this has already been considered, I'm very uneducated on the topic. If it has, could someone maybe link an analysis of the topic of lifespans and the like?