And some cells do not reproduce (neurons, etc), so you have to keep them in good shape, except this is impossible. For example 1/3 people are infected with Herpes virus which stays in their neurons.
In addition some cells reproduce only a few times, often only during youth.
No some cells never reproduce, for example motor neurons.
> "I imagine that if aging can be reversed new cell growth could also be stimulated."
I have a hard time to imagine how to replace a up to one meter/yard long cell with sometimes hundred of synapses which is surrounded by cells such as astroglia and microglia that are equally important.
In addition some cells reproduce only a few times, often only during youth.
And there is sometimes involution like in thymus.