"Or maybe anti-aging is inherently interesting to some people who want to live to see flying cars..."
Maybe anti-aging is inherently interesting? Do you not expect some people to want to survive? The will to live is inherent in humanity for very obvious evolutionary reasons. Moreover, anyone whose quality of life is positive has reason to want to live so long as that is the case. There are religious people who want to die so as to attain an afterlife, but unless you are hoping for Heaven/Nirvana/72 Virgins/whatever, or your current quality of life is negative, anti-aging should be inherently interesting to you.
"and no rational critique would dissuade them."
If something is inherently interesting, people will want it unless there is a cost that exceeds the benefit. If there is such a cost, such a rational critique will in fact dissuade rational people. This seems like a cheap attempt to make transhumanists seem unwilling to listen to reason without actually making a case to that effect.
"In short, the best approach would be to rebuild your tree from scratch. This is why having kids is more efficient than just having more time on earth."
More efficient for what purpose? Even if we assume you are correct that experience is a negative to career success (not what is typically observed, to put it mildly), what are you hoping to attain with your career that is better served by dying and hoping your children will carry on the work? It can't be making money for you-you do not benefit from money when you're dead! It can't be making money for your children; you're as dismissive of their survival as of your own. It sounds like you want money for your genetic lineage, but why? Normally people value their wellbeing and that of their family; all of you dying does not serve this. You can't even claim to be following some underlying evolutionary principle, as the survival of you and your children will preserve your genes better than letting them be diluted down over generations.
"Even if birth rates went down to replacement rate tomorrow, improvements in longevity would result in more people being on the planet at any given time."
Correct. On the other hand, while overpopulation is a potential concern with longevity, it is worth taking five minutes to consider the problem rather than simply electing to die. Potential solutions include interplanetary colonization, mind uploading, better birth control or simply handing off the problem to a friendly AI. All of these are technically challenging, but so is life extension. It does not make sense to assume that a world capable of it must be forever incapable of ever finding a solution to overpopulation. To assert that this question must necessarily make life extension harmful is to assert that we know that no such solution can be found, quite the extraordinary claim. The milder claim that this is a concern worth addressing is by contrast valid, but that's not a reason to abandon life extension, merely one to develop population solutions in tandem, if we can.
"Arguably, one of reasons young people are frustrated with modern politics is that boomers are still very much in the driver's seat. "
Easy enough to mandate political retirement at a particular age. Disenfranchisement is better than death. To quote Eliezer's short story Three Worlds Collide, "Only youth can Administrate. That is the pact of immortality."
"...we'll need more senior care. This may become a costly burden on future generations. "
Potentially. Or a population that spends more time healthy and able to work and less time slowly decaying in retirement might have a lighter burden on future generations. Or perhaps a growing, potentially-automated economy will obviate the question entirely. This is much like the overpopulation question in that it conflates desirability with prudence. Desirability is whether or not we consider a thing beneficial as such; whether or not we'd want it in the absence of countervailing costs. Prudence is whether or not we consider a thing worthwhile on net even counting the costs. You point out, correctly, that overpopulation and a strained senior care system are potential risks that may need to be addressed if we want to make life extension prudent. That does not mean that it is not desirable, nor that we should immediately view the costs it could impose as impossible to mitigate.
"We may also have to consider assisted suicide for people who would be dead if it weren't for technology. Should we keep them alive because we can?"
Do these people want to die? Are we out of resources to sustain them with? If the answers are no and no, why should we kill them? If one or more of the answers is yes, that's a concern, but one better answered by seeking to improve their quality of life or acquire more resources, at least if we value human wellbeing. And if we don't, why are we bothering to stay alive ourselves, or avoid killing willy-nilly?
Ultimately, it is human nature to value survival. We cannot always survive, we may sacrifice ourselves for others we care for if we cannot both survive, and some people even choose death out of misery or religious faith. Yet where it is possible, it is better to make life worth living than to give up and die. Where it is possible, it is better to save everyone rather than sacrificing our lives. Where it is possible, it is better to oppose aging like we would any other injury, and while I cannot claim that life is better than Heaven, you did not bring up afterlives, so it seems unlikely that they are factoring in your reasoning. Unless you assert that the natural order of things was divinely, benevolently ordained, there is no reason to think that death by aging is somehow better than any other threat to life, be it disease, injury, war, poverty or the like.
Would you use those same reasons to argue for Covid?