The Kaldor-Hicks argument is that a change in government policy which makes some people better off and some people worse off, should be pursued if the now-better-off people could in theory compensate the now-worse-off people. That is, the change should be enacted if it creates value. The compensation does not actually have to be paid. Changes which create value will make society better off, such as automation or trade liberalisation. If there is no systematic bias, then the winners and losers from various changes will tend to be random. If many Kaldor-Hicks improvements are made, then over time everyone will tend to become better off.
However, the Kaldor-Hicks argument does not work for redistribution. Consider a person from a poor background, who is intelligent enough to become a doctor but cannot afford the training. They work for many years in a menial job, saving enough money to train as a doctor. They are finally able to pay for their training and earn a higher salary. This is inefficient. One argument is that the state should pay for their training, without requiring the money to be repaid. That way, the person can start their work as a doctor much earlier, increasing their lifetime earnings. "Society as a whole becomes better off." However, this is not sustainable. In the short run, the total resources in the society increase, as the person provides their services as a doctor, and earns more money. In the long run, the extra resources are likely to be consumed, rather than reinvested into further training.
Why were the person's parents unable to pay for the training? Because, despite being presumably of similar intelligence to their offspring, they were spendthrift. The quality of spendthriftiness was presumably also inherited by their offspring. "Society" can divert resources into such a family, but over the long run they will be destroyed.
There is a Lindy alternative, which is that the person borrows money to pay for their training, and repays it out of their increased productivity.
Exception to this argument: state funding for eugenics such as embryo selection. At least in this case, improvements to intelligence are permanent, even if no improvements to spendthriftiness are made.