Its not that different then generational wealth, we have families in the west that have built up wealth for centuries. But imaging how the west is sliding faster and faster into neo feudalism having to life as a serf forever does make it seem dystopian.
But being immune to aging does give the human race other options where a 100 year trip might now be impossible if you can reach a age of 1000 a 100 year stellar trip might actually be acceptable.
Does makes me wonder how many memories can the brain actually store and not degrade. when you go into your 4th century will you forget your 2nd century slowly.