I know I have ignored something fundamental in my model.
The Kelly formula assumes that you can bet any amount you like, but there are only so many things worth insuring against. Once those are covered, there is no opportunity to spend more, even if you're still below what the formula says.
In addition, what is a catastrophic loss, hence worth insuring against, varies with wealth. If the risks that you actually face scale linearly with your wealth, then so should your expenditure on insurance. But if having ten times the wealth, your taste were only to live in twice as expensive a house, drive twice as expensive a car, etc. then this will not be the case. You will run out of insurance opportunities even faster than when you were poorer. At the Jobs or Gates level of wealth, there are essentially no insurable catastrophes. Anything big enough to wipe out your fortune would also wipe out the insurance company.
Your reply provides part of the missing piece. Given that I am over some kind of absolute measure of poverty, empirically having twice as much disposable income won't translate into twice as much insurable assets. This limits the portion of bankroll that can be spent for insurance. Also, Kelly assumed unlitimited offer of bets which is not that far from the truth. Theoretically I can ask the insurer to give twice the payout for twice the cost of insurance.
And still, your answer doesn't quite answer my original question. I asked for given (monthly) income, ...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.