They also defy logic; when you lend someone money, they should pay you a penalty for borrowing that money.

Only if they ask to borrow it. Banks today don’t need depositors’ money. They provide checking and safety service for a price, including the right to use the money should the opportunity arise, but negative interest rates imply that the opportunity to use the money does not support paying for the privilege. And what’s this “penalty” crap? I don’t pay my dentist a penalty for protecting my teeth. Why should a borrower pay a penalty for credit?

Interest rate cuts are kind of like a drug that stimulates the economy.

This is exactly backwards. Interest rate increases are like a drug that slows the economy. Withdrawing a drug can have negative consequences, but it’s not “like a drug.” Economies are bi-polar; interest rates keep them stable. Raising and lowering the dosage are way better analogies than treating changes in one direction as a drug as if the patient is at any time not on drugs at all.

The real danger of the Fed lowering rates too much is that the world will lose confidence in the dollar. Our idiot president’s indiscriminate use of sanctions is already scaring our allies out of trading in our currency. The dollar’s status as the world’s reserve currency is valuable; it enables us to borrow at low rates despite our huge trade and fiscal deficits. But if we abuse that privilege to achieve political ends, as opposed to financial gain, the privilege will go away. Add excess money-printing to the mix, and the result is a very low overnight rate and a dramatically steeper yield curve that chokes off long-term borrowing.

In short, there is nothing particularly special about negative interest rates per se except that they are very very low by historical standards and so may give rise to bad private underwriting and stupid public spending. Both of these can result in too much money chasing too few goods, and that’s a bad thing. OTOH, global capacity is expanding and marginal costs are decreasing, so it’s not clear just how much money is “too much” money. The ratio of debt/GDP used to be a good measure, but Japan is showing us that it really isn’t that good a proxy in today’s world. Trouble is, we don’t yet have a consensus on a better canary to put in this particular coal mine.