Unlike a pension, an annuity isn't tied to a specific employer, so it doesn't have career-immobilizing vesting requirements or weird payout rules tied to how much money you make in the last N years of your career. And you can select an annuity provider based on its fees and how solid its financials are, factors that aren't necessarily high on the list while selecting an employer.
So, why aren't annuities more popular as a retirement savings vehicle?