In a sense, rejuvenation would be a watershed moment like the development of agriculture. People living in agricultural societies were plagued with problems like malnutrition from poor diet variety and exploitation by states and tax collectors compared to their hunter-gatherer counterparts. But despite these problems, the world still became dominated by agricultural states because they could out-compete hunter-gatherers with their larger numbers and armies, force them off their traditional pastures, and convert those pastures to farmland.

If rejuvenated humans with centuries of experience are able to out-compete their younger counterparts then all the problems with stagnation in an immortal society would be a moot point. You could imagine this happening if rejuvenation preserved the mental capabilities of a 20-something well past 100. That would be decades of time to build up skill in politics, business, and technology, and to compete in such a society might well end up requiring decades of education and experience. Birthing a new person into this society would be a massive multi-decade investment to bring them up to speed that might require the resources of not just two parents but perhaps an entire extended family, which would be justified considering that any new member of this society will be around for centuries. People will be complaining in news columns about the stodginess and stagnation of their society, but proposals to limit the use of rejuvenation or allow younger members of society more power would be as outlandish as allowing a middle-schooler to become president. You simply can't compete without having 60+ years of experience, just like how hunter-gathers simply couldn't compete against a much larger agricultural population.

One thing I'd worry a lot about is stagnating in a moral/ideological sense, one of the few things guaranteeing change in political power is that no matter how powerful a politician is they'll eventually die and younger people that grew up differently have a chance to steer things.

Aging kills literally everyone. Sure, there will be problems when we stop it, but they won't be worse.

Advancing technology will help solve the problems of inequality too. In the same way that I have more luxuries than an ancient king, the poor of the future will (hopefully) live much better lives than the wealthy and powerful today, even if they're worse off than the wealthy and powerful of the future. Alternatively, ideas like "wealth" may erode as we get cheaper energy (fusion, better solar), better robots and AI. Productivity may go so high that everyone can have everything they want.

Nitpick, but not everyone dies of aging.

There are plenty of deaths due to violence and stupidity.