What you are describing is a safer strategy than the standard 4% strategy they criticise in their paper. The 4% strategy they criticise is the one where you take 4% of the capital you had at the start of your retirement, regardless of what happens to your investments thereafter. Unlike your version, that strategy can run out of money.
Your version still has some the problems though. Income is variable, so you are not maximising utility. (Each extra dollar you spend is assumed to buy things you value less than the one before, so if you spend $110 one year and $100 the next, $5 you spent in the earlier year is sub-optimal because with hindsight it would have bought something you wanted more in the second year.)
Also, if your investments do well and you don't buy an annuity at the right time, you will end up with a surplus that you can only spend on things that are less valuable to you than guaranteeing you don't end your days eating cat-food. Actually I think this is just the same problem I mentioned in the previous paragraph. The real problem with never buying an annuity is either running out of money or leaving money unspent, in this case only the second applies.