Well, I think there is more to it than that. The whole body is degenerating or "rotting" as we continue to grow older. Including that Mitochondria's primary function is to break down organic materials into energy. Mostly aging has to do with isolated cells that somehow start dividing/reproducing slower. You also have to account for DNA which I believe does tell when the body starts to degrade and eventually die.
Like if your family has a history of dieing at a certain age; most likely that will be passed on to you, though you would probably live longer since that time prolongs over extended periods of time.
It could be possible that the degeneration of the body has to do with being effected by the environment in which it can damage, mutate or destroy cells in a above average rate since cells are constantly being created and destroyed.
Also you have to consider that it is possible that even though you are able to regenerate limbs or organs that your brain is still aging. In that case, the aging process might go deeper than the conscious mind.
And like what someone said previously, our nervous system would not be able to withstand the regenerative process only IF it was instantaneous; like Dragon Ball Z.
If the regenerative process is slow then we probably would be able to withstand it.
Also cells do contain memory, just not in a sense that you can look at it and go âSoooooo thatâs what happened that night!â. The memory contained is nothing more than data which is in a form which we can not read; basically it is coded in a special language; although mostly memory is in a form of a Neurological Signal which is sent and interpreted by the brain. Though the cells do play a part in memory.
EDIT
I think if anyone went through a dramatic physical change in a matter of seconds, then I think they would be screaming from the tremendous amount of pain.