You say your spiel as though we haven't spent hundreds of years trying to move beyond dictatorships, empires, and dynasties that treat their citizens as chattel.

I don't know if care per se about economic inequality, but a singular group that's able to maintain and extend its status as an insular elite and accrue resources for timescales in excess of those outside its ranks is likely to have interests that become increasingly at odds with those of the everyday human with a shorter lifespan.

Now it'd be fine if rejuvenation became cheap and accessible to all, but I think there's a very real danger that it becomes available to an elite first, an elite which would then create barriers to such technology's spread as means of maintaining status.