If you wait to take your annuity, it has the same result as indexing. The payment to increase 2% per year.
Compare these two tables of a Regular Annuity and an Indexed Annuity.
Example of a Regular Annuity (non-indexed)
Print: Regular-Annuity.pdf
Print: Indexed-Annuity.pdf
The indexed payment is a lot less. It will take him 10 plus years to catch up with the amount paid by the regular annuity (non-indexed).
If you wait to take your annuity, you get the same poor result. The payments you don’t receive cannot be made up, even with increased payments. You saved the money to enjoy it later and now “later” has arrived. When you buy a house or a car, you look for the best deal. You should apply the same reasoning when you buy an annuity.