I've had thoughts along these lines. If there was a secret to extreme longevity, it would have to be carefully kept.
First, it's likely to be extremely expensive, and create murderous jealousy. I think it would be easy to find people denied life who would tear those in possession of the secret limb from limb.
Second, although I know the topic of birth control can upset some here (especially if it involves fetal termination) it is obvious that once people can live many generations, there would be an overcrowding problem. But, that's only true if the treatment is broadly available. Which gets us back to my first point. It just can't be, without some other things being agreed upon. Who would work dangerous, low pay jobs, endangering their eternal life? The treatment would have to be limited to a few.
Who would work dangerous, low pay jobs, endangering their eternal life?
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bots
Or: perhaps the longevity tech is also related to curing ills and disabilities, including trauma. So, how about this bargain: work the dangerous jobs that bots can’t yet handle and we’ll give you some version of the repair and extend tech?
Of course, in the interests of profit and elitism, at some point the PTB will cheat the underlings by limiting the results for them.
As for over-population: many articles lately resurrecting a year-old meta-study verifying male fertility is at an historic low. One such article inserted a hallelujah that it meant *starvation* was put off another decade or so.
Most common cause of low fertility in males: exposure to chemicals and pesticides, smoking and obesity. Only 15% of Americans still smoke. Do the math.