Investment rate of return is important, yes. But when it comes to life annuities, it is more important to look at the individual needs.
A lot people are going to retire with a decent sum of money, say somewhere between FRS and ERS range. The question on their mind should be, "How do I make this sum of money last for the rest of my life while enjoying my remaining years as best as I can?"
Without a life annuity, you will have to come up with your own drawdown strategy, and you will run into a dilemma. If you are too conservative with your drawdown, you won't be enjoying your retirement years as much as you would like before you depart this world. If you are too indulgent with your drawdown, you will likely end up running out of money at some age before you die and you will then have to depend on the charity of others.
And this is where life annuities come in - they take the guess work out of your drawdown strategy by applying actuarial principles and the pooling of funds. They charge a bit for the service and in return you get the peace of mind that you will receive a 'just right" regular income for the rest of your life that is somewhere between the two extremes I have described earlier.
Of course, not everyone will need life annuities. For quite a lot of people, they are happy to take a conservative drawdown because they have more money than their retirement lifestyle requires so they will never run out of money barring certain unforeseen circumstances. In this case, it will make more sense to try to maximize your IRR so you can pass more money on to your loved ones after you depart.
However CPF Life does provide additional value to people in this group, in that the money is guaranteed by government securities and protected from lawsuits, creditors and bankruptcy. If I say something wrong about the wrong people and get sued until my pants drop, the people coming for me can take away all my money in the bank and my investments but they cannot away my CPF Life. I'm not sure if they can liquidate anyone's private life annuities, perhaps that would depend on their surrender value.
For me, I project myself to have a sum of money substantially above the ERS when I retire, and I have more or less worked out that my best strategy will be to maximize the payouts of my CPF Life by topping it up to my ERS, delaying payouts until 70 and taking the escalating plan. With my remaining cash, I plan to enjoy my retirement by traveling and perhaps indulging in some more extravagant stuff, safe in the knowledge that even if I overspend and run out of cash, I still have my CPF Life to fallback into which should have escalated past the standard payout by the time I have run out of cash. If I die early, well my CPF Life may well have been a loss, but I won't be too troubled by that as a pile of ash, and my benefactors will still have a significant amount of my leftover cash to share among themselves.
Coming back to private annuities, I do not plan to get one as I expect the maximized CPF Life payout will be sufficient to support the minimum standard of living that I want to have. For people where the CPF Life payout is insufficient, I would say private life annuities are a good idea to set aside a sum so that the payouts on top of your CPF Life will support the standard of living that you need, and you can happily indulge away whatever money you have remaining.
So in conclusion, private life annuities are not useless. There are people for which this is a suitable and makes sense.