I think scientists currently are testing ways to "partially" reprogram cells to make them younger while keeping their function. Early studies in mice have shown some reversal of aging signs.
Seems like an engineering problem more than an absolute limitation.
This doesn't help overall. Mixing two roughly equally broken things just yields the mean of the two. But the trick is that roughly 60 to 70% of conceptions will not survive to birth. This rejection sampling is ultimately what makes children younger.
If you had a population of single cells that didn't undergo this rejection sampling at some point, entropy and Muller's ratchet would actually age the entire population and kill it.
What scientists usually mean by "cellular age" isn’t mutation load, it’s the epigenetic and functional state of cells. During gametogenesis and early embryonic development DNA undergoes extensive repair, telomere maintenance and global epigenetic reprogramming that wipes and rewrites methylation patterns. This resets the cellular "clock" even though some mutations are passed on.
So while mutation load drifts slightly each generation, the reason babies start biologically young is this large scale reprogramming. That’s also why researchers are trying to mimic this process in adult cells (Yamanaka factors etc) to reverse aspects of aging.