The reasoning is that as you gain information, you also have a duty to the people in the control group to use the best available information to take care of their health. Once you gain "enough" information ("enough" being statistically defined) that the drug helps, each additional person you let languish in the control group (who is denied access to the drug) is a cost that must be weighed against the benefit of getting additional information. When the data is clear enough, the cost can exceed the benefit, and you stop early.

Typically you'd register a "stopping rule" before you start your trial: a good drug often will trigger the stopping rule, as it helped so much that we learned about its efficacy on a smaller N than originally planned.

There are many different stopping criteria, depending on the trial (in safety trials you'd typically stop because you've found evidence that the drug is unsafe and continuing would be unfair to the folks in the treatment group, whereas in efficacy trials after safety has been established, you'd stop because you've found evidence that the drug is effective and continuing would be unfair to the folks in the control group).

The reasoning is money, the unreasoning is ethical sophistry.

Its typically an ethical decision. In the event of a deadly disease ( cancer, covid, hiv etc ) its considered harmful to continue giving a less effective treatment once you have shown some superiority/inferiority.

It’s both ethical and statistical. If you observe a strong enough effect, you can reach significance with less data. When people are dying, sometimes you throw a Hail Mary.

if you don't think the quality of the trial is so bad as to outright impair approval (and right now the political pressure for a tool, any tool, to fight COVID is so intense that there's zero chance it wouldn't be) then why continue? It costs money to do trials and it represents lost revenue where you could be the sole seller of the only known drug to treat a deadly pandemic.

in fact there is a downside risk to continuing as well, further study might show that the early results were an outlier and the drug is not as effective as previously thought (or has some serious side effects in some situation), and then you lose all the money you've invested. But if you push it through, there is no risk of being sued since the US Government has waived any liability on the part of drug companies for these therapies.

in a game-theoretic sense there is absolutely no benefit to continuing the trials and potential downsides to doing so. Remember, for-profit companies don't care about maximizing public health, they care about maximizing revenue. Especially when you've explicitly removed all financial liability for being risky with public health.