We're already kinda going on that way with transplants, cures for most diseases and stem cells researches, but even if we were able to switch your entire body for a new, shiny one right now, your brain would still be dying, so unless you can find a way to stop it from dying or to make it recover lost cells, you'd still end dying or being with serious problems in your brain sooner or later.
If this was achieved, I don't think being sterilized by force/in trade of it would be a good idea. As long as people have some good sense (and they will have a lot more by the time they are old than when young), they won't be wanting a lot of kids. One of my favorite games had a race that lives a lot say something about humans which I sort of agree: Their lifes are so short, that they don't bother thinking about the long term result of their actions, because they won't see it anyways. I kind of agree with that, if people got biological immortality, they would grow very old and be much more knowledgeable and experienced as the time went by, and less bond to make stupid mistakes, they would think more about their future, and that includes having kids. They would think better about it and the weight of that decision, and perhaps want to get sterilized by choice, or only have one or two kids.
The only "bad" thing I can see happening with it is people getting bored after some time and wanting to end their lives. And I put bad in quote marks because it was their choice to live longer, their choice to end it, so its not necessarily a bad thing.
Cures are no longer being developed, not because the technology is lacking, but because of the greed of both the doctors and the pharmaceutical industry. If there is no profit in finding a cure, then there is even less reason to promote research into immortality.
I'm sorry, but where did you get that idea from? Does the increase in curable diseases over the decades say anything to you? Or all the tests and experiments being made out there? You're also disconsidering those who contribute or research by pure interest and not by money interest. And even if they were only driven by money, if they find the cure of something, then they can sell it and profit.
After all , the only reason why life is so precious is because we are mortal , take that away and you take away everything that make life so great .
My view on it is different than that: Life is precious because I only have one, not because I will lose it. And I want to enjoy everything I can out of it. By achieving immortality that would just give more time to enjoy it, but I would still have just one.
Lets say you got a cake, and there is only one of it, you can't have another. It would be good to enjoy it as much as possible, because you only have one, not because it will end after you eat it. And if you can get a bigger cake, then better! More to enjoy.