BRAINS AGE, TOO.
There will come a point that having a young body will do absolutely nothing to help your decrepit brain. Senility anyone?
And if you have means to de-age the brain, why not just de-age the rest of the body with it? Really, it's not like the parts are somehow sui generis in a way that would let you do one and not the other.
(to be sure, even if you could rejuventate yourself, it would still not be immortality. Heat death of the universe will get you, if nothing earlier does.)