We would not.

The extra amount you need as life expectancy increases diminishes with each extra year. E.g. let's assume (for each of calculation only; you can just scale it up linearly) that you need 10k/year on top of social security to live off in retirement. If your savings is 100k, and you only get a 5% return every year, you'll run out after about 15 years. Hence a typical lifetime annuity bought at age 65 will be around that in the US because it matches up with current US life expectancy (it won't deviate much elsewhere).

So that's for living to roughly 80. Here's how it'll play out as you approach 120:

85: ~20% more 90: ~38% more 95: ~52% more 100: ~62% more 105: ~70% more 110: ~77% more 115: ~82% more 120: ~86% more

As you can see, the curve flattens out. It flattens out because you're getting closer and closer to have sufficient money that the returns can sustain you perpetually (at a 5% return, which is pretty conservative, at $200k, you can perpetually take out $10k, and no further increase in life expectancy will change that).

Now, that of course is not in any way an insignificant increase, but if we assume 40 working years, $100k is about $850/year additional investment + compounding investment return at 5%. $186k is around $1550/year compounding.

But here's the thing, if you work 10 years longer, you grow it disproportionately much, because you delay starting to take money out, and you need less, while you get the compounding investment return of ten more years, and that drives down the yearly savings you need to make back down to around $850/year.

So an increase of 40 years of life expectancy "just" requires 10 more years of work to fully fund it assuming the same payment in during the later years. But here's the thing: Most people have far higher salaries towards the end of their careers, even inflation-adjusted, so most people would be able to fund 40 more years with far less than 10 extra years of work.

(Note that if you already were on track for your pensions to last you to 90, if you were pre-retirement now, you'd "only" need about 35% extra savings to have enough until 120, because you'd get returns from a higher base, so the extra savings or extra years of work needed over what you managed would be even lower)

These all work on averages btw. - due to differences in health, this is where we really want insurance/state pensions rather than relying on individual contributions.

This doesn't mean there aren't problems to deal with. Especially if the life expectancy grows fast enough that it "outpaces" peoples ability to adjust. But it's thankfully not quite as bad as having to add another 30 years of work.