Plus infinite life seems a near super power. Would they just hand it to nobodies? Seems like at that point they could produce a special few that live forever while the rest of the plebs have a largely normal life.
And heck, to extend your idea further; if it is equally difficult than perhaps you could do both, not one or the other. So make many mortals and a select few chosen royalty bloodlines that live forever. You get a population you can predictably control and forever royalty.
.. sometimes i'm glad i wasn't born 500 years later.
So the whole economic structure would have to be very different. Maybe AI’s will be specifically designed to serve humans, and maybe they’ll design particularly rebellious humans, as they present more novel requests.
Of course the technology might never get there either but to me gene editing for a birth defect sounds easier than gene editing to live forever but maybe i underestimate the former.