I agree that "what is the monetary value of your life?" is not the same question as "how happy are you?", and so far as I can tell no one was saying otherwise.

Presumably the two are related; if you are miserable and expect to remain so, you will probably be less willing to pay for more life. Clearly the two are not the same; if you have no money, your ability to pay will be greatly constrained.

You can deal with that latter problem to some extent by asking hypothetical questions: suppose your net wealth were exactly $1M, then how much would you pay for a 0.1% reduction in your chance of dying this year? But of course people don't necessarily have that much insight into what they would do in hypothetical situations. Or by asking people what they would pay for other people's lives, which is kinda what e.g. national healthcare institutions like the NHS in the UK or Medicare in the US have to do to decide what treatments they are willing to pay for. But of course that also isn't measuring happiness, nor even other people's estimates of it.

Or, of course, you could use the same techniques as you use for calculating a "statistical value of a life" to put a value on things other than merely being alive or not. Ask people about things that trade off money against some probability of disfigurement, depression, being abandoned by their spouse, etc., etc. Or look at the tradeoffs they actually make.

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If you have capital but no income then you can buy life insurance, at least until the capital runs out. Of course, if you have capital then you can also buy income.

I agree that retirement income is still income, which is why I bothered to add "even if you have no income". (Of course being retired and having no income of any sort is a highly unusual situation, because there are state pensions and the like.)

But, I repeat, it is simply not true that the only possible reason for buying life insurance is to make up for the loss of your income after you die. Here is a concrete situation to imagine:

You have some investment that provides income. It will continue to do so after you die. It's enough for you to live on, reasonably comfortably but not at all extravagantly. Your needs are few, so you don't take a job, you just live off your investment income.

The investment will not change as a result of your death. No one will be financially worse off when you die. But you have an aged parent who needs a lot of help: something like one person, full time. You do it for free -- you have plenty of time and you love them and care about them. But there is no one else who would be willing and able to do it for free.

So when you die, your parent will need a lot of help, and it will need to be paid for. They can inherit that investment and the income it brings, but that may not be enough to pay for the help they need. You are still fairly young and healthy, so you can get life insurance cheaply. That way, if you get hit by a bus or have an unexpected heart attack or something, your parent will be able to afford the care they need.

(This is a situation in which life insurance is bought for a reason other than replacing income. It is not a situation in which life insurance is bought by someone who has no income to be replaced. Those are separate possibilities, and I suspect there is no plausible scenario in which they both happen at once.)