Someone once suggested (not sure if s/he wants credit for the idea; will change this if s/he does) that an infinite life-span would not be very useful. Why? Because the way our knowledge is structured would become so out-dated that it would both be much easier to start over (teach a blank mind from scratch) and also too difficult to be worthwhile to fix current, old people. Now, in the future there will be all sorts of great technologies to help fix people with bad ideas, and a whole profession of people very good at helping with this sort of thing, so what was meant was not that it'd just be a bit too expensive, but rather that it would be a virtually impossible or actually impossible task. So difficult that in millions of years of progress it would still seem impossible.
How could this be? Sure, I may have some hangups (I hate eggs and math textbooks, for example), but I'm sure a hundred years with no pressures, lots of friends, and various nice futurey things could cure me. And if it couldn't, the next thousand years might. As it is, I already like math in certain forms, and have come to like some foods I used to hate. So there's nothing remotely impossible here.
OK let's try something else. What if I grew up thinking the world was flat? Would that be a problem? Well, certainly for many people this was a misconception they never really dealt with during their natural life-spans. But some people did solve it. And I don't see why the rest couldn't get over it eventually. They could circle around the world, then go into space and look at it, so they could see for themselves that "scientists" weren't just playing a prank. And they could learn more physics than we know today, and see how well it works.
Now some people might be tempted to, by now, say the idea of infinite life-spans being useless is nuts (if they didn't decide that much earlier). But this would be immoral. For we've still shown absolutely no understanding of what was meant! Now, we could assume nothing remotely sensible was meant. But that's just no way to discuss philosophy. We should either say we don't know and aren't interested, or look to understand the subject.
Thus far we've looked at hangups and misconceptions that can be expressed in English. But only the simplest hangups and misconceptions can be. Anything that we can put into English, our entire society already has some understanding of.
But try to imagine. We are very young, and we begin to encounter various problems. We try to conjecture the answers. But randomly conjecturing answers with no constraints on what we think of is unlikely to solve many problems. It'd be like if the answer was 8 and we rolled a die with an infinite number of sides, trying to find that answer. So what we do is make conjectures about what sort of answers we are looking for. For example in the dice analogy we might conjecture that useful answers are mostly under 1,000,000,000. And now for many sorts of problems (the ones where our conjecture is about right) we will find the answers much more easily.
Next up, we might notice that for certain classes of problems, more specific constraints are useful. Problems about wood are mostly between 1-3 million. Problems about sand 7-10 million. Now we might solve most problems more accurately and faster (as long as our constraints are good). Of course some constraints will turn out wrong, but we can change them. At least at first. But what if we have a system 200 layers deep. Is it about earth? ok < 1,000,000,000,000 Is it about sand? no, ok not btwn 7-10 mil. Is it about water? yes, ok look between 44-999 mil. is the water cold? yes, ok, look at odd numbers only. etc etc
Of course real constraints are much more complex, because answers do not lie on a number-line. Anyhow, imagine our first 10 layers have not changed since we were 5. The next 80 have not changed since we were 20. Now go forward in time thousands of years. Our problem situation is very, very different than it was when we were growing up. And instead of 200 layers, we have 2 million. But, our situation is very, very different now than it was as we grew up. And half our layers are dead wrong, including the 3rd and 9th ones. Is it really feasible to fix this? Without becoming a new person?
And it gets worse. At the thousand year mark, when we moved to a new planet, our system of constraints started to fail a bit. So we added some new modifications to fix things on top of the whole system. These increased our problem solving abilities and kept us functional. And going through just a couple more layers was so negligibly inefficient as not to be a problem. But they were only ad hoc modifications, so after some time started to function poorly. So we added more. And more. And after living a million years, it's quite possible we've been making things progressively worse for most of that time. Sure we've been learning new things the whole time, but to fix the actual heart of our problems, we would have to change some of our most basic ideas that have become more and more distant from our latest modifications.
Now, I'm currently unconvinced this analysis actually implies the conclusions we were looking for (that an infinite life-span would not be valuable). But it's not an unreasonable conjecture either, and certainly not nuts, even though prima facie it does sound a bit nuts. And extensive further argument would be required to reject it.
Oh, just for fun, count how many life extentionists have ever gone through this analysis. I don't think you'll need your toes.