I'm intrigued as to what state structures their payouts that way.
Others will give you Math answers, but I'll give you my gut reactions.
By forgoing the pension until 50 or 62, you are in affect giving up the option to retire early. Now maybe you have significant savings on the side. But most people would consider 220k a large portion of their Stash. I certainty don't include my pension in my FIRE numbers because it won't kick in until well after I'm retired. A 220k lump sum now could make a significant step towards retiring in the next decade.
The 3% return they are offering you is ok, but only what a 30 year bond pays. If you just took the lump sum and bought the bond you'd get the same result, have control, and leave it to your heirs. RMDs could be a problem, but you'll roll that to a Roth soon enough.
The annual benefit of 11.5k is worth an equivalent of 287,500 assuming a 4% withdraw rate. You can't claim that for 11 years. You can privately invest 220k and turn it into 287k in 10 years, that's a 2.7% return per year. Heck dividends alone may get you there. Likewise the rate of return for claiming the pension at 62 is 4.8%.
So net-net it sounds like all their numbers are very conservative, and by taking the lump sum and buying a bond, much less stocks you can get equal treatment. Most pensions are back loaded, so if you return, your benefits may rise much quicker. Other things to consider are how much you are saving on the side, your risk profile (but like i said 30 year bonds), and your ability to make a investing statement and stick to it.