That seems rather dubious. It would be wonderful if society were organised to maximally channel the efforts of all the warm bodies available, but (bizarrely in my view) "not enough jobs to go around" is seemingly a thing. Also, "more people alive" certainly does not equal "cheaper healthcare" no matter how you slice it.
That aside, it seems to me that a more immediately realizable method of achieving that goal would be to redistribute wealth to the enormous fraction of the world that cannot afford even basic medical care - even in the United States.
It seems highly likely to me that even if it were possible to extend human lifespan by some substantial degree with no ill effects, this technology would probably not be used on everybody in the world, or on every social class. This would come with grave destabilising effects. You'd struggle to find a better way to foment resentment and revolution than today's super-powerful and mega-rich becoming immortal as well.
It's possible that if mortality rates were reduced really dramatically, some population activists would get upset (and I've seen indications of that in other threads here).
When a bureaucrat sitting behind a desk can use a rubber-stamp to tell an elderly person, "Nope, no treatment for you this time, you're done," there's nothing to stop more and more people from being denied treatment. Eventually even younger people with mental illnesses or genetic disorders will be eliminated--all to avoid overcrowding and overloading of the health care system, of course.
It's for the greater good. Don't you want to be a good citizen? Reduce your burden on society, today!*
*Cremation fees not included.
SENS approach is essentially suggesting something better than that. According to them, pouring billions of dollars into individual age-related diseases (e.g., age-related onset of cancer) is the wrong way to go, because age-related diseases are a symptom of the root cause, which is aging itself, defined to be molecular and cellular damage through out the body. If that is tackled head on, there would enourmous savings in health care costs (both maintenance and research) and a positive impact on the economy as a result of more healthy people being available for work.