We don’t know this. We know of no creatures as biologically complex as humans that demonstrate biological immortality. That might be because nature never bothered. It might be because it can’t.
But you are generally correct: we have strong evidence healthspan-increasing interventions are not only possible, but proximate. That research could move faster with more funding, particularly from the public, since if we relinquish this funding to the rich it will not prioritize treatments which may be slightly less effective but much cheaper and thus broadly applicable.
(1) Yes we do have an example: us. Why is a baby’s cells young and healthy, and not the age of the parents? Dormant eggs are not the answer as you’d still get accumulating damage over time. Turns out there are mechanisms for cellular reprogramming which rejuvenates cells. There are mechanisms for making ages cells indistinguishable from young cells. We just haven’t fully harnessed this capability on therapeutics yet.
(2) The deeper point is one of logical necessity. No bird flies faster than the speed of sound, yet that doesn’t work as an argument for the impossibility of the SR-71 or Concorde. No physical law prevents restoring tissue to healthy young state. We just haven’t developed the tools to do so (yet).
You’re speculating too far beyond what we know to speak so definitively. Plenty of biology and even thermodynamics suggests there may be limits. That doesn’t prove they exist. But it’s in the same category as saying there are no know physics which prohibit time travel or transcending the human condition into a state of pure consciousness. Like, sure, there aren’t, but to use your analogy, ancient Romans didn’t know about the speed of light.
Diseased old cells have accumulated damage in a multitude of different forms, as well as accumulated junk. Fix the errors and remove the junk. It is as easy and as hard as that.
Nothing in thermodynamics or organic chemistry prevents this from being possible in principle.
Thermodynamics is not a limit on an intelligent agent reconfiguring atoms on Earth for the next several billion years.