I understand you don't have to spend it, but what I don't understand is why you're "living on last month's income" at all. What does the income have to do with it?
Instead spend what you will, and earn what you can. Keep a buffer if your income is erratic.
What does the phrase "spend last month's income" add, or even mean?
In other words, honest question: Does your spending vary based on the previous months income?
If yes, I'd argue you're doing spending wrong.
If no, and your spending doesn't vary based on the income, isn't "live on last month's income" completely meaningless?
Think of it not as last month's income, but changing the definition of is what is in my 'available to spend, save, or otherwise do monetary things with' bucket. For you, that is likely your checking account balance at any given time. Given your circumstances and low spending, that makes perfect sense. For others, having that number defined over a month rather than on a per paycheck basis, even if they save the exact same amount, is what they prefer.
My spending does not really vary. What I choose to save for does. If I have lots of overtime, I fill the buckets for the rainy day funds more than I would otherwise and try to max out the Roth a little earlier, or send a little more to the mortgage. My spending on food, necessities, and wants does not change very much, if at all. To turn the question on it's head, would you consider this the "wrong" way to save?
Regarding "living on last month's income" being meaningless, do you still have the same question when you use the working definition above? For most Mustachians I would imagine it's just a buffer in the checking account so we don't have to worry about direct deposit errors, seeing a really low balance in the account, or double checking sending money to investments as soon as we get the funds available.
Once you pass the initial out of paycheck cycle, it becomes a streamlined way to see your finances on a monthly basis. It also means I'm more comfortable using the Roth as my emergency fund, because if need be I can tap the buffer.