It's very dangerous for US, China and even Russia alike if lower tier powers suddenly are justified in randomly using nukes just when they're at disadvantage.
It will give small countries an unacceptable level of strength at the negotiating table. Imagine who will be next to acquire and then use nukes against their political enemies. Iran? Some African dictator? Everyone will be rushing to make nukes, and those who can't make nukes will make dirty bombs.
Hell, North Korea today has a more developed nuclear program than Israel, and they can take the peninsula in a week if they spammed nukes. They can nuke a supposedly more powerful nation like Japan, and there's precisely nothing Japan can do about it.
All this is going to break the monopoly of large scale violence that the big 3 currently have. Without nukes, no one can credibly invade without huge military, intelligence and supply chain assets. With nukes, even a weak country that can't take a Chechnya sized area like Israel can credibly threaten regional powers. Or NK destroy SK despite SK being more developed.
If US has any modicum of self preservation, it's keeping those Israeli nukes under lock and key, only for the eventuality of extreme indiscriminate state/ethnic group threatening violence against Tel Aviv. The same way China has mostly kept Pyongyang's warheads.