Depends. I say you can create your own annuity. If we define annuity as "any mathematical scheme that insures income for longer than any reasonable measure of life expectancy", then I say I agree. (that's just a definition I made up ).
I would define an annuity as an agreement among a group of people that those who die sooner than expected will leave their money to those who live longer than expected.
With this agreement in place you do not need to plan to make your money last 5/10/15 years past your life expectancy, therefore your income is much, much higher than it would be without the agreement.
It is completely impossible to "create your own annuity", if you go it alone your income will unavoidably be significantly lower.
(When comparing returns from traditional annuities with the income you generate from investing yourself, remember to assume you self-invest in the same kind of assets, typically government bonds. Otherwise you are not comparing like with like, in terms or risk and return.)
Some people are rich enough that they can be fairly sure they won't go through all their money no matter how long they live, and the value to them of leaving bequests is higher than the value they place on increasing their standard of living. These are people for whom not buying an annuity is sensible.